No, there is no general rule about involuntary motion, it entirely depends on the spell.
There is, however, a general distinction between when a spell talks about a creature moving into versus a creature entering the spell's area.
Movement is a defined game mechanic. When a creature moves, it's doing so of its own volition:
On your turn, you can move a distance up to your speed.
Spells like prismatic wall and guardian of faith specify effects when a creature moves to within a certain range.
Any creature hostile to you that moves to a space within 10 feet of the guardian for the first time on a turn [...]
By contrast, most area of effect spells don't use the word "move," instead they use the phrase "enters the spell's area," like cloudkill:
When a creature enters the spell's area for the first time on a turn or starts its turn there, [...]
While "moving" is a specifically defined game mechanic, "entering an area" isn't, so it only has the meaning the phrase naturally does in the English language, which doesn't require it to be voluntary. You can be pushed into a moonbeam and immediately suffer the consequences.
The Sage Advice Compendium specifically clarifies this point:
Entering such an area of effect needn’t be voluntary,
unless a spell says otherwise. You can, therefore, hurl a
creature into the area with a spell like thunderwave. We
consider that clever play, not an imbalance, so hurl away!
In this specific case, the spell spike growth says:
When a creature moves into or within the area, it takes 2d4 piercing damage for every 5 feet it travels.
If a creature is pulled by thorn whip or otherwise moved by someone else, it isn't using its movement, and it doesn't take damage from the spikes.
But surely this is a meaningless semantic quibble?
You would think. It seems unnatural to assign special meaning to the word movement, and 5e generally favors natural language. But the way the designers use the words move and movement in some places and very conspicuously avoid them in others implies otherwise. It at least implies it's not NOT a keyword and they made an effort to keep the door open for making it one.
The Shove action and a fighter's Pushing Attack say you 'push' the target. The thorn whip cantrip says you 'pull' the target. Grappling says you 'drag or carry' a creature. Virtually every area denial spell, and all Crawford tweets & Sage Advice, talk exclusively about the wording of when a creature 'enters' the hostile area.
https://twitter.com/JeremyECrawford/status/575817883109826560
When a spell's description uses "enter" in relation to an AoE, the entering has to be voluntary only if the text says so.
And if a distinction between moving and entering didn't exist, they would never have bothered to nerf the create bonfire cantrip: they replaced the usual, standard wording, identical with moonbeam and just about every other area denial spell that costs a spell slot, with the phrase 'moves into' in errata.
https://media.wizards.com/2016/downloads/DND/PotA-Errata.pdf
In the fourth sentence, “enters” is changed to “moves
into.” In addition, this new paragraph appears after the first
paragraph: “The bonfire ignites flammable objects in its
area that aren’t being worn or carried.” (future printing)
Either:
A) this published change to the spell's wording did absolutely nothing except exclude the extremely rare edge case of an enemy unwittingly teleporting into a magic bonfire they aren't expecting at their unseen destination (because they cast dimension door and you somehow predicted their precise destination?), because teleportation isn't movement, or
B) the wording change was genuinely meaningful because it also nerfed the strategy of combining create bonfire with potentially multiple allies using grappling, the Shove action, or a fighter's Pushing Attack maneuver to force an enemy to enter and re-enter a magic bonfire on multiple turns in a round, all without expending a spell slot.
