です is the polite form of is/am/are/be. It can also come after adjectives to make a sentence polite. ます is an ending attached to verbs, and functions to make the sentence polite.
これは猫です。
This is a cat.
今日は暑いです。
Today is hot.
ケーキを食べます。
I eat cake.
Note that in the second example although the translation contains the word is this is contained in the adjective 暑い = "be hot". です does not mean is when it comes after an adjective, it just makes the sentence polite.
In the third example the verb 食べる (dictionary/plain form) becomes 食べます to make it polite.