Contact: friction between objects (or between a fluid and an object); push/impact of an object onto another…
Non-contact: gravitational pull between celestial bodies (stars, planets, satellites, asteroids, comets…); magnetic force between 2 magnets held apart; bending of an electron stream by a magnetic field in an old CRT display…
Note that if you were to “z<oo>m in” to atomic and subatomic scales, then the contact forces could generally be seen as non-contact repulsive forces between the cloud of electrons of one atom and that of another atom (and more rarely as attractive forces between an atom's or ion's nucleus and the electrons of another atom). But the concept of contact vs. non-contact forces is meant to be used at regular (and not atomic/subatomic) scales.
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Contact: friction between objects (or between a fluid and an object); push/impact of an object onto another…
Non-contact: gravitational pull between celestial bodies (stars, planets, satellites, asteroids, comets…); magnetic force between 2 magnets held apart; bending of an electron stream by a magnetic field in an old CRT display…
Note that if you were to “z<oo>m in” to atomic and subatomic scales, then the contact forces could generally be seen as non-contact repulsive forces between the cloud of electrons of one atom and that of another atom (and more rarely as attractive forces between an atom's or ion's nucleus and the electrons of another atom). But the concept of contact vs. non-contact forces is meant to be used at regular (and not atomic/subatomic) scales.