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In this video,
If you look closely, you can see the smaller planet deforming before the actual collision. I think I remember a term existed for this. I think it is similar to Spaghettification, but for just normal planets and similar objects. Maybe it's called 'X distance,' where X is some word I cannot remember or could be something else.
The generic term is tidal deformation. At a distance of ~385000 km, the Moon subtly distorts the shape of the Earth. Those distortions are readily visible in the Earth's oceanic tides, and not quite as readily visible in the Earth's solid body tides (but still quite observable with good instrumentation). The Sun also causes tides on the Earth, about half as strong as those caused by the Moon.
These tidal distortions can in some cases rip bodies apart. A nice example was comet Shoemaker–Levy 9, which was captured by Jupiter, then later ripped apart into at least 21 pieces, which then collided with Jupiter in a well observed series of events. The comet eventually fell well within Jupiter's Roche limit, thereby causing it to be torn into pieces. Even more extreme cases involve relativistic as well as Newtonian distortions. As noted in the question, this extreme form of tidal distortions results in spaghettification.
The Roche limit is an approximation of the distance to a strong gravitational source at which a smaller body might be torn apart by gravity. If a body is composed of small particles that are bound together by self gravitation only, tidal distortions might well rip the body apart if it gets too close to a strong gravitational source.
Comets are loosely connected chunks of smaller pieces of ice and minerals that are collectively bound together mostly by gravity. The smaller pieces of comet Shoemaker–Levy 9 were bound chemically as well as gravitationally; this is why I called the Roche limit an approximation. The 21 (or more) smaller pieces remained intact until they collided with Jupiter's atmosphere.
Could you be thinking of the Roche limit? From the link:
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation.[1] Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit, material tends to coalesce.
