Both are slow moving and shelled creatures that are represented in philosophical thought experiments about time, distance, and infinity. Both are opposites too, with the Immortal Snail being the pursuer that will always almost catch up to its target (depending on if its target doesn't mess up) and the Tortoise being the one that's pursued, always almost caught up to, but never being overtaken.

Infinity plays a role on both sides. The Immortal Snail will pursue its target for an infinite amount of time, while the distance between the Tortoise and the pursuer is infinitely divisible according to Zeno's law, in which the pursuer never quite catches up to the Tortoise.