Time travel causes headaches. And not just because of the grammar. Here's the way I look at it:
Picard A commands the Enterprise-D
in the timeline where Tasha Yar A is killed by the living tar pool. When the Enterprise-C
goes through the time rift, reality shifts and it is Picard B who encounters them. Tasha B goes back in time, which in turn creates Picard C--native to a universe all-but-identical to that of Picard A.
Picard A still exists in his own timeline, one where Commander Sela never existed (although someone else might well have played her "role" in history).
Aside from all this is Picard D, whose timeline of the Federation at war with the Klingons but into whose timeline the Enterprise C
There's also a Picard E, almost identical to Picard D save for some reason the Enterprise C
didn't make it back into the past to change history.
All of these exist, but in their own timelines. TNG followed the adventures of Picard A and then those of Picard C.