reach vs achieve

reach is a noun but achieve is not a noun.

Word	Noun	Adjective	Verb	Adverb
reach	Yes	No	Yes	No
achieve	No	No	Yes	No

As verbs, achieve is a hypernym of reach; that is, achieve is a word with a broader meaning than reach:

Other hypernyms of reach include accomplish, attain, reach.

As verbs, reach and achieve are synonyms defined as:

Other synonyms of reach include accomplish, attain.

reach (noun)	achieve (noun)
the act of physically reaching or thrusting out
an area in which something acts or operates or has power or control:
the limit of capability
the limits within which something can be effective

reach (verb)	achieve (verb)
be in or establish communication with	to gain with effort
to exert much effort or energy
move forward or upward in order to touch; also in a metaphorical sense
reach a point in time, or a certain state or level
reach a destination, either real or abstract
reach a goal
place into the hands or custody of
to gain with effort
to extend as far as