Is the part pointed out by red arrow a stud?
The part pointed at by the blue arrow is a "doubled top plate".

In this case, the wall it's on top of is a load-bearing wall. You can tell because the inner ends of the ceiling joists rest on it. If you pulled that center wall out, there would be nothing to support the top plate and therefore nothing to support the overlapped, inner ends of the joists. Pulling that wall would end up causing collapse of the structure. Handy for demolition, not so much for a simple remodel.

It may well be load-bearing even if the joists run all the way from outer wall to outer wall - that would depend on the height of the joists. Are they tall enough (and therefore strong enough) to span the full width if that wall were removed? To make that determination, though, would require looking at the structural design of the building, and might require the services of a structural engineer for confirmation before removing that center wall.