Push-up vs.Press-up

Solution 1:

"Press-up" is definitely the British version of "push-up". I had to learn to change my wording after moving down under from North America.

Solution 2:

They are one and the same thing, although "press-up" is British whereas "push-up" is American.

The online Oxford dictionary says of "push-up": Another term for press-up. Chiefly North American

And of "press-up": An exercise in which a person lies facing the floor and, keeping their back straight, raises their body by pressing down on their hands:

@nxx's answer is interesting about using "press-up" in Oz. I always assumed that "push-up" was the British usage, since that's what we say here in South Africa, and we used to be a British colony.