You can just say „czekaj” (imperfective, just focusing on the act of waiting), but „zaczekaj/poczekaj” (perfective) focus on the fact that the waiting is a finite action and you won’t have to stand waiting forever. So the perfective forms may be a bit more polite.
The prefixes „za-” and „po-” are indeed distantly related to the prepositions „za” and „po”, but that doesn’t mean that their meanings are related in an obvious way.
The prefix po- generally means “to do something a bit/for a while”, as in pochodzić, porobić… so logically „poczekać” means „to wait a bit”.
The prefix za- generally expresses finality. An extreme example would be „bić” (to beat), „pobić” (to beat up), „zabić” (to kill). However with a simple action like “waiting” there’s not that much room for such nuances; „zaczekać” and „poczekać” mean almost exactly the same and you can safely treat them as synonyms.