punch press vs mechanical press

punch press and mechanical press both are nouns.

Word	Noun	Adjective	Verb	Adverb
punch press	Yes	No	No	No
mechanical press	Yes	No	No	No

As nouns, mechanical press is a hypernym of punch press; that is, mechanical press is a word with a broader meaning than punch press:

punch press: a power driven press used to shape metal parts
mechanical press: any machine that exerts pressure to form or shape or cut materials or extract liquids or compress solids

Other hypernyms of punch press include press.

punch press (noun)	mechanical press (noun)
a power driven press used to shape metal parts	any machine that exerts pressure to form or shape or cut materials or extract liquids or compress solids