Muscles themselves can only pull, retract, etc.
Everything is technically pulling at all times always. But is contracting equal to pulling; and is pushing equal to expansion ? Or are we defining it based on the weight's angle ? movement ? joint angle ? muscle angle ? muscle length before and after ? theres too many factors.
What is defined as a "press" or a "pull" is really quite subjective.
As just the general way we usually tend to "think" about things, I would say that anything moving weight towards your body's center of gravity while resisting gravity/tension is a pull and moving away from your body's center of gravity or at-least close to direct or straight angle of your center of gravity, also of course resisting gravity/tension is a press.
The dead is a press with the legs until they are straight, then a pull with the back to reach a maximum height at the hips. but the hams are basically pulling to "press" the legs, as are the quads ? so do you consider the legs as a unit ? individual muscles ? muscle groups ?
Its both a press and a pull by most definitions, and those definitions are not defined.
Again, all muscle can only contract, so your defining press and pull based on angles and changing definitions depending on how you view the body's methods of generating force.
Its impossible to say really much besides what past people FEEL it should be defined as, because mechanically its too complex to state without a clear definition, and coming up with one is literally impossible since a blanket statment of "everything is technically a pull, or pulls" doesn't seem "correct" to most people.
And a more accurate definition is impossible due to how the body functions in conjunction.