retreat vs move back

retreat is a noun but move back is not a noun.

Word	Noun	Adjective	Verb	Adverb
retreat	Yes	No	Yes	No
move back	No	No	Yes	No

As verbs, retreat and move back are synonyms defined as:

Other synonyms of retreat include draw back, pull away, pull back, recede, retire, withdraw.

As verbs, move back is a hypernym of retreat; that is, move back is a word with a broader meaning than retreat:

Other hypernyms of retreat include draw back, pull away, pull back, recede, retire, retreat, withdraw.

retreat (noun)	move back (noun)
(military) withdrawal of troops to a more favorable position to escape the enemy's superior forces or after a defeat
withdrawal for prayer and study and meditation
the act of withdrawing or going backward (especially to escape something hazardous or unpleasant)
an area where you can be alone
(military) a bugle call signaling the lowering of the flag at sunset
(military) a signal to begin a withdrawal from a dangerous position
a place of privacy; a place affording peace and quiet

retreat (verb)	move back (verb)
make a retreat from an earlier commitment or activity	pull back or move away or backward
pull back or move away or backward
move back
move away, as for privacy