P union Q will equal the set of all vectors coming from either P or Q.
P + Q will equal the set of all vectors that look like p + q, where p in P and q in Q.
Sp ( P union Q ) will equal the set of all linear combinations of vectors coming from P union Q.
1 and 2 are not necessarily the same, I wouldn't think: the zero vector of one space need not be the zero vector of another space, although the zero vector of any given space is unique.
That's all I have time for right now.