More (plural)

Example:

I have more horses.

Plures, Plura

Example:

Plures equos habeo.

Plures is an adjective that takes the case of the noun it modifies, in this case Accusative.

More (singular)

Example:

I want more food

Plus, Pluris, n (for the singular)

Example:

Plus cibi peteo.

Plus is a noun that uses a partitive genitive to complete its meaning--cibi is genitive.

It is used when you would make the thing plural.