Push, shove, thrust, propel mean to use force upon a thing so as to make it move ahead or aside.
Push implies the application of force by a body (as a person) already in contact with the body to be moved onward, aside, or out of the way.
Shove often differs from push in carrying a stronger implication of the exercise of muscular strength and of forcing something along a surface.
Often, when muscular exertion is not strongly implied, haste or roughness or rudeness in pushing is suggested.
Thrust differs from push in carrying a weaker implication of steadiness or continuousness in the application of force and a stronger suggestion of rapidity in the movement effected or of violence in the force that is used; often the use of actual physical force is not clearly implied.
Often, also, it implies the sudden and forcible pushing (as of a weapon, implement, or instrument) so that it enters into the thing aimed at.
Propel implies a driving forward or onward by a force or power that imparts motion. In some use it implies pressure exerted from outside or behind, usually by some power that is not human.
Additionally, it is the usual term when the use of a mechanical aid or of an actuating power (as steam or electrical power) is implied.
In extended uses push implies a pressing or urging forward (as with insistence, with vigor, or with impetuousness) so that one’s end may be gained, one’s work may be completed, or one’s goal be reached.
Shove often suggests obtrusiveness or intrusiveness or lack of finesse in attaining an end or making a way for oneself or another.
Thrust implies a forcing upon others of something that is not wanted, desired, or sought for.
Propel is sometimes used in place of impel when a strong inner urge or appetite is implied as pushing one on, especially toward what one desires.