This has nothing to do with Latin, but okay...
Your question isn't quite clear to me. By "this kind of relationship" I suppose you mean pederastic relationships? In that case, no, these words are not specific to pederasty in Ancient Greek. The word ἐραστής (erastes) can refer to any type of male lover, or by metaphor even to a strong adherent of something, e.g. ἐραστής τυραννίδος "lover of tyranny". Hence the usual pairing is ὁ ἐραστής "the lover" and ἡ ἐρωμένη "the beloved", i.e. the traditional male/female relationship.
The masculine form ἐρώμενος (eromenos), on the other hand, could only mean a male beloved, but I don't think that necessarily meant beloved to a male (though in most cases it probably would). Ἐρώμενος and ἐρωμένη are just the respective masculine and feminine present passive participles of the verb ἐράω "to desire/love sexually".
To be honest, I don't know whether the Greeks had such precise terminology for the individuals in a pederastic relationship. A lover of boys in general was of course called παιδεραστής (paederastes), a literal compound word equivalent to "boylover". Plato uses φιλεραστής for the boy-beloved in his Symposium, but I couldn't say whether that was a common term or just a nonce word on his part (it literally means something like "fond of being loved"). Of course the Romans used the term catamitus, from which we get the English word "catamite".