In the following sutta the Buddha clearly says he is not a human, deva etc. Rather, he is awakened.
Although we have the term "enlightenment" in English, the more precise term based on the Pali original is "awakened" (Buddha).
The phrase "and so, brahman, I'm awake" (Ven. Thanissaro) also translated as "and so, brahmin, I am a Buddha" (Ven Sujato) comes from the Pali "tasmā buddhosmi brāhmaṇā”ti".
The suttas are discourses, spoken either by the Buddha himself or by his most senior disciples and, was kept alive and recited in full by his senior disciple Ven. Ananda, after the Buddha's passing, in the First Buddhist Council. Then later, it was passed down through generations of monks through memorization and chanting.
Also: deva is god or angel, gandhabba is fairy, yakkha is native spirit.
Then the Blessed One, leaving the road, went to sit at the root of a
certain tree — his legs crossed, his body erect, with mindfulness
established to the fore. Then Dona, following the Blessed One's
footprints, saw him sitting at the root of the tree: confident,
inspiring confidence, his senses calmed, his mind calmed, having
attained the utmost control & tranquility, tamed, guarded, his senses
restrained, a naga. On seeing him, he went to him and said,
"Master, are you a deva?"
"No, brahman, I am not a deva."
"Are you a gandhabba?"
"... a yakkha?"
"... a human being?"
"No, brahman, I am not a human being."
"When asked, 'Are you a deva?' you answer, 'No, brahman, I am not a
deva.' When asked, 'Are you a gandhabba?' you answer, 'No, brahman, I
am not a gandhabba.' When asked, 'Are you a yakkha?' you answer, 'No,
brahman, I am not a yakkha.' When asked, 'Are you a human being?' you
answer, 'No, brahman, I am not a human being.' Then what sort of being
"Brahman, the fermentations by which — if they were not abandoned — I
would be a deva: Those are abandoned by me, their root destroyed, made
like a palmyra stump, deprived of the conditions of development, not
destined for future arising. The fermentations by which — if they were
not abandoned — I would be a gandhabba... a yakkha... a human being:
Those are abandoned by me, their root destroyed, made like a palmyra
stump, deprived of the conditions of development, not destined for
"Just like a red, blue, or white lotus — born in the water, grown in
the water, rising up above the water — stands unsmeared by the water,
in the same way I — born in the world, grown in the world, having
overcome the world — live unsmeared by the world. Remember me,
brahman, as 'awakened.' (Buddha)
"The fermentations by which I would go
to a deva-state,
or become a gandhabba in the sky,
or go to a yakkha-state & human-state:
Those have been destroyed by me,
ruined, their stems removed.
Like a blue lotus, rising up,
unsmeared by water,
unsmeared am I by the world,
and so, brahman,
Dona Sutta (AN 4.36)
The Buddha also described himself as a "fully awakened Buddha" (sammāsambuddha).
If you’ve gone to a wilderness, or to the root of a tree, or to an
empty hut and you get scared or terrified, just recollect me:
‘That Blessed One is perfected, a fully awakened Buddha,
accomplished in knowledge and conduct, holy, knower of the world,
supreme guide for those who wish to train, teacher of gods and humans,
“itipi so bhagavā arahaṁ sammāsambuddho vijjācaraṇasampanno
sugato lokavidū anuttaro purisadammasārathi satthā devamanussānaṁ
Then your fear and terror will go away.