wander vs play around

wander and play around both are verbs.

Word	Noun	Adjective	Verb	Adverb
wander	No	No	Yes	No
play around	No	No	Yes	No

As verbs, play around is a hyponym of wander; that is, play around is a word with a more specific, narrower meaning than wander:

Other hyponyms of wander include two-time, fool around.

wander (verb)	play around (verb)
lose clarity or turn aside especially from the main subject of attention or course of argument in writing, thinking, or speaking	commit adultery
move about aimlessly or without any destination, often in search of food or employment	work with in an amateurish manner
to move or cause to move in a sinuous, spiral, or circular course
go via an indirect route or at no set pace
be sexually unfaithful to one's partner in marriage