Door knob installation direction
What you ask, all depends on who made the latchset. Some make it where the screws are horizontal, others make it so they are vertical as you have. 

I think Schlage and Kwikset are an example of this.

The same may be true for the lock. In some cases on some locksets, the part where the tang of the lock has two options to place it, on horizontal lock, the other, vertical lock. This may or may not be your case. This is more often seen with deadbolts with thumb turns.