The exercise where you jump from a squat position and then do a push-up is a burpee.
A standard burpee usually begins standing, drops into a squat with the hands on the floor, sends the feet back into a plank, returns them beneath the body, and finishes by standing. Many modern versions add a push-up in the plank position and an explosive jump at the top, matching the movement described in the question.
The exercise is named after American physiologist Royal H. Burpee, who developed an earlier four-count version as part of a fitness test. His original movement did not necessarily include the dramatic jump and push-up commonly seen in contemporary workouts. The squat-thrust portion is the transition from the squat to the plank and back.
Burpees are often confused with jump squats because both include an upward jump. A jump squat does not include the plank or push-up. Mountain climbers keep the body in a plank while driving the knees forward, and lunges use a split stance rather than a floor-to-standing sequence.