The difference between Non-count and Uncountable

When used as adjectives, non-count means uncountable, whereas uncountable means so many as to be incapable of being counted.

Uncountable is also noun with the meaning: an uncountable noun.

check bellow for the other definitions of Non-count and Uncountable

Uncountable as an adjective:

So many as to be incapable of being counted.

Examples:

"The reasons for our failure were as uncountable as the grains of sand on a beach."
Uncountable as an adjective (mathematics):

Incapable of being put into one-to-one correspondence with the natural numbers or any subset thereof.

Examples:

"Cantor’s “diagonal proof” shows that the set of real numbers is uncountable."
Uncountable as an adjective (grammar, of a noun):

Describes a meaning of a noun that cannot be used freely with numbers or the indefinite article, and which therefore usually takes no plural form. Example: information.

Examples:

"Many languages do not distinguish countable nouns from uncountable nouns."

"One meaning in law of the supposedly uncountable noun "information" is used in the plural and is countable."