Are there quadruplet cards in Magic the Gathering?
The phrase you're looking for is "functional reprint" - they're not literally reprinted cards, but they're functionally the same.

There's a list of them on MTG Salvation. You can just skim through the table and look for cards with lots of reprints. Generally cards like that are pretty boring, for example vanilla creatures. Simpler cards tend to make sense in more sets, and the renaming happens when the old name doesn't fit thematically with the set they want to print it in.

Some of the most-reprinted cards:


Grizzly Bears (1G, 2/2): Barbary Apes, Balduvian Bears, Bear Cub, Forest Bear, Cylian Elf, Runeclaw Bear (except not all of those are bears)
Hill Giant (2R, 3/3): Tor Giant, Ogre Warrior, Barbarian Horde, Wild Jhovall, Canyon Minotaur, Lagac Lizard, Russet Wolves (except most of those aren't giants)


(There are plenty more creatures that have been functionally reprinted a few times; some even have exciting abilities like flying or mountainwalk!)

And I think the most-reprinted noncreature spell (though I didn't go through the list too carefully yet) is Remove Soul (1U, "Counter target creature spell"): False Summoning, Preemptive Strike, and Essence Scatter. (Note that Preemptive Strike is from Portal Three Kingdoms and thus the wording on the physical card is really really awkward, but the oracle text is the same.)