The Smith machine weighted push-up is a pushing movement performed with a plate resting on the back or shoulders. It is performed most safely with a foot or so of space at the bottom to minimize the risk of getting "pinned" under the bar. It targets all the same muscles as a push-up, including the chest, triceps, and shoulders.
Simple way to overload push-ups when body weight becomes too easy
Can be performed in strength and muscle-focused rep ranges
Can be loaded heavier than push-ups with weight vests or plates on the back