In r/Buddhism, there’s some people who take up the semantic correction. To me, I just stick to rebirth. I don’t bother much about the semantics. When I post rebirth evidences, and people click, they read: reincarnation evidences, I don’t mind. Cause those evidences are from external (non-Buddhist) sources.
When people argue that it’s for reincarnation, not rebirth, I tell them that both are the same when you look at it from external evidence wise. They only differ in philosophical explanation of the phenomenon. Reincarnation typically connotes an immortal soul. Rebirth without soul, you’ll have to go deep into dependent origination etc.
But functionally, they are the same. Reincarnation people just didn’t properly study non-self if they believe in a soul. If you take two lifetimes, linked directly via rebirth, you can see many things (memory/kamma/ ignorance/ birthmark-to-fatal-wound) are passed on to the next life. So, if the perspective is limited to this, people naturally take what’s the same as the soul.
However, when you expand to many many lifetimes (beginning-less in Buddhism), not 1 thing remains the same throughout the rebirth going to the lowest realms, insects, spiders, to humans, to the highest gods, Sakka, Mara, Brahmas, even formless realms. We all had been there before, and given even only 1% change for each rebirth, all of the 5 aggregates for everyone had completely changed countless times since beginningless rebirth. No immortal unchanging soul is found in this picture.
Most people are only concerned with their immediate next life. Functionally, there seems to be no difference.
Those who are too averse to the soul idea (which can be a useful shortcut to collect what’s being passed on in rebirth), they may also reject certain things in Buddhism, like the in-between states, after death, before rebirth, which the EBT supports, but Theravada don’t. Cause the in-between person sounds too much like the soul. They rather think of them as rebirth in peta realm. This is not supported as anagami (who cannot be reborn in lower realms) can attain to final liberation in the in-between states.
Some people reject rebirth, by saying that literal rebirth is reincarnation, but they believe in rebirth, which is something different and they totally ignore the rebirth/reincarnation evidences. They are actually siding with secular Buddhism on no literal rebirth.
Yes, I think that the stronger battle ground is to get Buddhists to reply with rebirth evidences to those doubters of rebirth/reincarnation rather than to have semantic correction.