According to my experience, there are two main meanings of the term "mind" in Buddhist context. It's important to understand those meanings, in order to avoid confusion and misconceptions.
First meaning is "mind in general", which means limitless space where all the reality manifests.
It's related to notions of Buddha-mind, Dharmakaya, Universal Mind, Consciousness.
There are many kinds of consciousnesses. In the philosophical Buddhist tradition of Chittamatra (or Cittamatra), which means "Consciousness Only", there are eight consciousnesses. (Some schools count few more or less).
These eight consciousnesses are:
The five primary - the consciousnesses of:
The sixth is the mental consciousness, which processes the data from the previous five. Our practice deals with this, the sixth consciousness. Sometimes it might be referred as "mind".
The seventh is manas. As I understand, it's like consciousness in post-freudian psychology: a part of the space centered on our personal perceptions.
The eight is alaya-vijnana, or Store Consciousness. I understand it as limitless ocean where our seventh consciousnesses floats like a crystal ball.
Alaya-vijnana stores our karmic seeds - imprints of past actions - kinetic energies of our intentions.
It is related to the notion of vijnana as the fifth group of phenomena (dharmas). (The fifth skandha).
Please don't feel overwhelmed with all these concepts. They are just pretty simple ways to describe our experiences. If you study them in practice, it all becomes not so complex.
Note that for the most part I spoke of consciousness rather than mind; I distinguish these terms.
So basically the first major meaning of "mind" is limitless space where dharmas appear.
Perhaps the most important and praised philosophical school of Buddhism, Madhyamaka ("Middle Way"), emphasizes emptiness of all phenomena, conditional nature of all notions and objects.
Even the mind - as that limitless space, or in any other meaning - is not really existent. (Though also not really non-existent).
In that sense, Buddhists speak of awakening as realization of No-Mind. As long as we cling to ideas of mind or self or whatever else, we rely on the level of ideas, production of the sixth consciousness, rather than the original reality.
Therefore, what is actual Buddha-mind? Nothing real. Not even that limitless space I mentioned before.
In awakening, we see all such things as mental generalizations, nothing more.
Now what is the second major meaning of "mind"?
When Zen teacher asks you, "What's your mind?" - what would you answer?
Maybe you would describe your experience you are living through, right now.
In that sense, "mind" is the experience now. It can be clouded, with vexations, or very clear and bright...
This meaning of "mind" relates somehow to the notion of consciousness from Twelve nidanas (links of dependent origination).
Consciousness from Twelve nidanas is depicted as monkey jumping among fruits on a tree. From one fruit to another. It's consciousness engaged in activities formed by samskaras (mental constructing).
Being limited by our mental creations, consciousness becomes entangled in samsara.
So liberation can be explained as dropping the limits of mental constructions, opening the mind to being unlimited, dropping even the notions of "mind" and "unlimited" and "awakening" and "liberation".
I'm not sure I answered the question completely - as you see, I have no idea what they meant by "nine meanings of the term mind".
Theories are endless. I hope I pointed at some key ideas which can help you in the practice.
Use the mind well, and through practice of exploration you will always find some useful understanding, eventually helping all beings in liberation.