Re cross vertical or diagonal, flag terminology derives from that pertaining to shields, and thus historically from Norman French.

A cross with vertical plus horizontal arms is referred to as a cross. Rotated to diagonals it becomes a saltire, thus the flag of St Patrick would be blazoned "argent, a saltire gules".

The Scottish use of the same symbol, but differently coloured, is very well known, so much so that many believe that many mistakenly believe that theirs is the only saltire around.