The difference between Countable and Infinite

Countable as an adjective:

Capable of being counted; having a quantity.

Countable as an adjective (mathematics, of a set):

Finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.

Countable as an adjective (mathematics, of a set):

Countably infinite; having a bijection with the natural numbers.

Countable as an adjective (grammar, of a noun):

Freely usable with the indefinite article and with numbers, and therefore having a plural form.

Infinite as an adjective:

Indefinably large, countlessly great; immense.

Infinite as an adjective:

Boundless, endless, without end or limits; innumerable.

Infinite as an adjective:

With plural noun: infinitely many.

Infinite as an adjective (mathematics):

Greater than any positive quantity or magnitude; limitless.

Infinite as an adjective (set theory, of a set):

Having infinitely many elements.

Infinite as an adjective (grammar):

Not limited by person or number.

Infinite as an adjective (music):

Capable of endless repetition; said of certain forms of the canon, also called perpetual fugues, constructed so that their ends lead to their beginnings.