In physics, we speak of forces applied to objects. This is all part of Newtonian mechanics. The key is that an object at rest will remain at rest unless a force acts on it, and an object in motion will continue in motion at the same speed (velocity) and in the same direction unless a force acts on it.
Forces can be categorized in various ways. A pull would be a force towards that which is pulling. A push would be a force away from that which is pulling.
Forces can also be categorized by whether contact is needed for the force to act on the object. An example of a pulling force with contact would be where I attach a rope to something and pull it towards me. Pulling can also be called attraction. An example of a pushing force with contact would be a billiard ball being hit by the cue ball and moving away from the cue ball. Pushing can be called repulsion.
There are also forces that act with no contact. The force of gravity is an attractive force only. Things fall towards the Earth when we let go of them due to gravity, and the earth stays in orbit around the sun instead of flying away in a straight line due to gravity. There is no gravity of repulsion, where objects are pushed apart due to their mass. Or at least, we haven't found one yet.
Electromagnetic force can attract (pull) or repel (push). Two magnet will attract from the north pole of one to the south pole of the other, but repel if the alignment is north-north or south-south.
Many forces can act at once, and forces come at odd angles, too. A cue ball will repel the ball it hits. But only if it hits straight on (with the line of travel of the cue ball the same as the line from the center of the cue ball to the center of the ball being hit) will the ball being struck move straight away from the cue ball. If the collision is at an angle, the push will occur, but it will be at an angle, and only some of the force will transfer.