

Basically, yeah, if you include all of their memories and experiences. The EMHs in the dilithium mines were EMH copies but weren’t The Doctor. I’ve also wondered if they were sentient or just good facsimiles. Part of The Doctor’s story arc was growing beyond his original EMH programming (plus B’Elanna expanding his matrix in some pretty hacky ways). So that leads me to believe that they weren’t sentient, though they had the potential to become so.
Anyway…
That said, the Doctor from “Living Witness” was, if I recall, the Backup EMH and had all of the The Doctor’s memories and was fully sentient as a result.
Essentially it would be the Will / Thomas Riker transporter accident equivalent for holographic beings




























It’s one of the “just bugs me” aspects of Trek in general, but they generally don’t make a distinction between sentience and sapience and use them interchangeably.