In the video, the speaker said:
Vedanta is about Atma (the Self). ... the next word is Sakshi (Witness) ... What
is the Self? Is it this bundle of flesh and blood? Is this person in
the body? The mind, the intellect, the memory, the likes and dislikes,
the knowledge, the person I think I am - is that the Self? Or is it
something beyond that? According to Vedanta, you are the real Self, is
the Witness-Consciousness. It is that which experiences. It is that
which experiences in the waking state, in the dream state, in the deep
sleep state. The one unchanging experiencer, which enables all
experience. What does that mean?
Take a simple methodology. It's a philosophical enquiry into who am I?
... This technique is called the seer and the seen. ... Remember, the
purpose is to discover the Atma, the real Self. It's about discovering
who you really are. ... It says: You are that which experiences. That
which is experienced, is not you (the Atma). ...
The speaker goes on to explain how the body, sensory organs, feelings, thoughts, and mind is that which is experienced, so it is not the Self. He says the Self is the Witness-Consciousness. He says you are not the person (which is the ego-identity or ego-personality constructed by the mind) - you are that which is aware of the person. He calls it the illuminer of the body-mind. He calls the Atma unchanging, while all the changing things are that which is experienced, not the experiencer.
Somewhere further in the video, he says Buddhist Madhyamaka has emptiness but even that emptiness must be experienced by a Witness-Consciousness.
Then further on, he goes on to explain what Advaita teaches, which is that all the changing things are not separate from Brahman, but rather manifested from Brahman and experienced by it. He provides the example that one witnesses the contents of one's dream, but the dream is also part of the mind and not separate from it. Then he says that God is the experiencer through all beings.
OP: Are the differences between Advaita Vedanta and Buddhism merely semantic/perspective? ... having studied Buddhism and Advaita
Vedanta, I've seen that the differences between the two are almost
non-existent.
The answer depends on what you define as Buddhism.
If you look at Mahayana Buddhism, I would say different Mahayana schools have different opinions.
From the following statement from this page, we see an explanation of Yogacara philosophy that sounds similar to Advaita Vedanta, yet is not exactly the same. This answer shows how Yogacara is different from Advaita.
The central thesis in the Yogācāra philosophy, the theory of the two
truths echoes is the assertion that all that is conventionally real is
only ideas, representations, images, creations of the mind, and that
there is no conventionally real object that exists outside the mind to
which it corresponds. These ideas are only objects of any cognition.
The whole universe is a mental universe. All physical objects are only
fiction, they are unreal even by the conventional standard, similar to
a dream, a mirage, a magical illusion, where what we perceive are only
products of our mind, without a real external existence.
All these arguments based on the facts of experience show that
objects do not exist really outside the mind, that they are products
of mental creation and that their appearance is entirely mind
dependent. Therefore the Yogācāra's theory of the two truths concludes
that the whole world is a product of mind—it is the collective mental
actions (karma) of all beings. All living beings see the same world
because of the identical maturation of their karmic consequences.
Since the karmic histories of beings are same, there is homogeneity in
the way in which the world is experienced and perceived. This is the
reason there is an orderly world instead of chaotic and arbitrariness.
This is also the reason behind the impressions of the objectivity of
the world.
... The idealism of Yogācāra holds nondual mind as the only ultimate
reality and the external world as merely conventional truths.
The same page explains Nagarjuna's Madhyamaka (below). Based on the following, it is clear that Advaita Vedanta is incompatible with Madhyamaka, because Madhyamaka advocates groundlessness i.e. everything is empty of intrinsic essense, including consciousness and emptiness itself. On the other hand, in Advaita Vedanta, Brahman is the substratum or ground for everything (see Vivekachudamani 225-231, 289).
There is absolutely nothing that has intrinsic essence in Madhyamaka, not even consciousness, not even emptiness. Empty of intrinsic essence does not mean unreality or non-existence, but is rather because everything is conditioned, changing and dependently originated.
On Nāgārjuna's Madhyamaka all things including ultimate truth are
ultimately unreal, empty (śūnya) of any intrinsic nature (svabhāva)
including the emptiness (śūnyatā) itself, therefore all are
groundless. In this sense a Mādhyamika (a proponent of the Madhyamaka
thought) is a an advocate of the emptiness (śūnyavādin), advocate of
the intrinsic unreality (niḥsvabhāvavādin), groundlessness,
essencelessness, or carelessness. Nevertheless to assert that all
things are empty of any intrinsic reality, for Nāgārjuna, is not to
undermine the existential status of things as simply nothing. On the
contrary, Nāgārjuna argues, to assert that the things are empty of any
intrinsic reality is to explain the way things really are as causally
conditioned phenomena (pratītyasamputpaṅhā)
Nāgārjuna's central argument to support his radical
non-foundationalist theory of the two truths draws upon an
understanding of conventional truth as tied to dependently arisen
phenomena, and ultimate truth as tied to emptiness of the intrinsic
nature. Since the former and the latter are coconstitutive of each
other, in that each entials the other, ultimate reality is tied to
being that which is conventionally real. Nāgārjuna advances important
arguments justifying the correlation between conventional truth
vis-à-vis dependent arising, and emptiness vis-à-vis ultimate truth.
These arguments bring home their epistemological and ontological
correlations ([MMK] 24.14; Dbu ma tsa 15a). He argues that wherever
applies emptiness as the ultimate reality, there applies the causal
efficacy of conventional reality and wherever emptiness does not apply
as the ultimate reality, there does not apply the causal efficacy of
conventional reality (Vig.71) (Dbu ma tsa 29a). According to
Nāgārjuna, ultimate reality's being empty of any intrinsic reality
affords conventional reality its causal efficacy since being
ultimately empty is identical to being causally produced,
conventionally. This must be so since, for Nāgārjuna, “there is no
thing that is not dependently arisen; therefore, there is no such
thing that is not empty” ([MMK] 24.19, Dbu ma tsa 15a).
From this page (quoted below), Candrakirti (a Madhyamika) criticizes Yogacara:
One further Buddhist movement that Candrakīrti criticizes is the
Yogācāra school, which he presents as advocating a form of subjective
idealism. Their claim that the world of experience is consciousness
only and that the contents of consciousness cannot be objects external
to consciousness itself is supported by several texts within the
Mahāyāna scriptural tradition. Candrakīrti explains these scriptures
as examples of teachings that the Buddha gave to counter a particular
kind of commonly held wrong view. There are, says Candrakīrti, those
who mistakenly believe that all their suffering is due to causes
outside themselves; they see themselves as unfortunate victims of a
hostile world. The Buddha, wishing to make it clear that the
predominant factor in dissatisfaction is the way one thinks about
one’s experiences, said, in effect “It’s all in the mind.” It would be
a mistake to take that statement literally and to conclude that
nothing but consciousness exists and that the world of experience that
feels as though it is external to consciousness is in fact produced by
consciousness or is inseparable from consciousness. The Yogācāra
offers good reasons to show that the contents of consciousness are
conditioned and therefore are empty of inherent existence, but they
fail to appreciate that exactly the same can be said of awareness
itself. In other words, says Candrakīrti, the Yogācāra philosophers
fail to acknowledge that everything, including consciousness itself,
is empty.
Also the same page (quoted below), mentions Santideva's (a Madhyamika) criticism of Yogacara:
Although beautifully written, Bodhicaryāvatāra does not display much
philosophical originality. Its principal contribution is in offering a
concise recapitulation of the currents of Madhyamaka thought and of
Madhyamaka arguments against Yogācāra monism, which portrays
consciousness as the ultimate source of all realities.
But what did the Buddha himself teach? From his own words in the Pali Canon (MN 38):
"Just as fire is classified simply by whatever requisite condition in
dependence on which it burns — a fire that burns in dependence on wood
is classified simply as a wood-fire, a fire that burns in dependence
on wood-chips is classified simply as a wood-chip-fire; a fire that
burns in dependence on grass is classified simply as a grass-fire; a
fire that burns in dependence on cow-dung is classified simply as a
cow-dung-fire; a fire that burns in dependence on chaff is classified
simply as a chaff-fire; a fire that burns in dependence on rubbish is
classified simply as a rubbish-fire — in the same way, consciousness
is classified simply by the requisite condition in dependence on which
it arises. Consciousness that arises in dependence on the eye & forms
is classified simply as eye-consciousness. Consciousness that arises
in dependence on the ear & sounds is classified simply as
ear-consciousness. Consciousness that arises in dependence on the nose
& aromas is classified simply as nose-consciousness. Consciousness
that arises in dependence on the tongue & flavors is classified simply
as tongue-consciousness. Consciousness that arises in dependence on
the body & tactile sensations is classified simply as
body-consciousness. Consciousness that arises in dependence on the
intellect & ideas is classified simply as intellect-consciousness.
The Buddha rubbished any notion of a permanent independent universal consciousness and explained how consciousness is linked to the six senses (including intellect).
From the same sutta:
The Blessed One then asked him: “Sāti, is it true that the following
pernicious view has arisen in you: ‘As I understand the Dhamma taught
by the Blessed One, it is this same consciousness that runs and
wanders through the round of rebirths, not another’?”
“Exactly so, venerable sir. As I understand the Dhamma taught by the
Blessed One, it is this same consciousness that runs and wanders
through the round of rebirths, not another.”
“What is that consciousness, Sāti?”
“Venerable sir, it is that which speaks and feels and experiences here
and there the result of good and bad actions.”
“Misguided man, to whom have you ever known me to teach the Dhamma in
that way? Misguided man, have I not stated in many ways consciousness
to be dependently arisen, since without a condition there is no
origination of consciousness? But you, misguided man, have
misrepresented us by your wrong grasp and injured yourself and stored
up much demerit; for this will lead to your harm and suffering for a
long time.”
Here, the Buddha says there is no such thing as permanent consciousness that experiences everything. Rather, it is dependently originated. Please also see this question.