In Titus 1:5, Paul writes that he left Titus in Crete to appoint πρεσβυτέρους (commonly translated 'elders') in every town:
"This is why I left you in Crete, so that you might put what remained into order, and appoint elders in every town as I directed you" (Titus 1:5 ESV)
In Titus 2:2, he goes on to explain how Titus should teach the πρεσβύτας, and then also the πρεσβύτιδας in 2:3.
"But as for you, teach what accords with sound doctrine. Older men are to be sober-minded, dignified, self-controlled, sound in faith, in love, and in steadfastness. Older women likewise are to be reverent in behavior, not slanderers or slaves to much wine. They are to teach what is good..." (Titus 2:1-3 ESV)
I understand that πρεσβύτερος is the common word used for 'elder' throughout the New Testament, and seems to have an occasional gender ambiguity built into it (Heb 11:2, also LXX Gen 18:11 for Abraham and Sarah), similarly to how ανθρωπος may mean man or woman. We know that the 4th Century Council of Laodicea wrote an article pertaining to 'women elders' (πρεσβύτιδας), but I'm unsure whether this kind of use of language was around in the first century or was just a later innovation.
Given the similarity of these three words in Titus, is there a clear distinction between the three as being referenced as different groups of people, or is it at all likely that the first term (1:5) simply a catch-all for both genders and then the next two (2:2,3) are then gender-specific?