No, they are different.
"Pushing the envelope" is a shortened form of "pushing the outside of the envelope." It was a phrase used by test pilots and it entered general use through Tom Wolfe's book about the space program, "the right stuff." "The envelope" means an outline on an engineering chart that graphs parameters--like airspeed and altitude--against each other. The envelope outlines all the combinations that have been tested and within which the plane behaves properly and can be flown safely. Somewhere outside the envelope are combinations that are dangerous--the plane might stall, or go into a spin, or the wings might come off. "Pushing the outside of the envelope" is test-pilot understatement. It means "I'm going to try something nobody has tried before, something a little outside the bounds, and see what happens. If the plane doesn't crash, we will add that point to the chart and the envelope becomes a little bigger."
In common parlance, it means "to try something bold," or "to go a little outside the known safe limits." For example, a child might "push the envelope" by using bad words in front of his parents to see how they react, and just how bad the bad words really are.