Off-beat playing is a case of syncopation, but syncopation includes more than off-beat playing.

Both terms refer to playing accented notes in places other than the strong down beats, e.g. other than beat 1 and 3 in case of 4/4 tempo.

Offbeat however mainly refers to the other *down* beats, the weaker beats, (e.g. beat 2 and 4 in typical 4/4 time), while syncopation could be anywhere, including on the "and" (e.g. anywhere except 1 and 3 in:  1 and 2 and 3 and 4 and)

E.g. in the first bar of "*I Can't Get No Satisfaction*" the accent on beat 2 is off-beat (and a syncopation),  and the accent on the "and" after beat 4 is another syncopation, but not an off-beat (it's not on 4, but on the "and" after 4)

Having said that, these are not scientific terms like botanical plant names... different people use these words interchangeably and/or with their own spin and interpretation. For example, another answer suggests that off-beat means playing slightly after the precise beat, for effect, while I would call that "*playing behind the beat*". And, to be sure, playing behind the beat is not a case of syncopation, it is something else entirely (e.g. think of a slow blues where all the notes are played on the strong down beats -- i.e. no syncopation -- but "lazily", i.e. slightly after the beat. That's playing behind the beat, but not syncopation)