I consider Xcross to be either:
1) seeing the direct solve to the Xcross during inspection
2) seeing the solve for the 2x2x2 and one other cross edge during inspection, with intention to locate and place the 4th cross edge during the solving phase.
3) seeing the solve for the 2x2x2 during inspection while making sure that the solution for the 2x2x2 puts the other 2 cross edges in a "good" position. A good position means easy to solve in relatively few moves.
4) Seeing the solve for the cross during inspection that either builds or preserves a c/e pair. For these solves you usually know how to place the pair during inspection as well.
5) Seeing the solve for the cross and one corner during inspection, with intention to locate and place the F2L edge during the solving phase using keyhole.
6) Seeing the solve for the cross and one F2L edge during inspection, with intention to locate and place the corresponding corner during the solving phase using keyhole.
Chris
I agree with his statements.
Feryll already posted what I feel counts as all types of what makes an X-cross. I personally would call a 2x2x2 start, with no pre-planning on the other pieces, to be a Petrich solve. Petrich is a very old term for Petrus-turned-Fridrich.
I would argue that if you plan only the 2x2x2 during inspection, but during the solve discover a nice continuation to make it become an X-cross, that it should probably still count as an Xcross. If you plan only the 2x2x2 during inspection, and then place the other cross edges one at a time, it's probably a Petrich solve. Either way, though, this is an incredibly gray area and depends on the person, and how they want to define X-cross.
Whether a solve is termed a Petrich or Xcross solve is not necessarily an important distinction though, the point is that you are utilizing block building to make an easier F2L than a standard cross + 4 pairs approach. So either way it is a good strategy, and can be worth a second or two saved, but the terminology I think is not necessarily as important.
My $0.02,
Chris