What qualifies as a slime has rarely varied. I have seen some taxonomies list jellyfish, shoggoths, chaos beasts, etc as examples of slimes. The only thing they all have in common is a lack of an internal skeleton and a lack of specifically bilateral symmetry: jellyfish are radially symmetric, whereas shoggoths and chaos beasts lack any symmetry.
Although even that commonality vanishes when you include WarCraft's take on oozes. For some reason they have a tendency to incorporate the bones of prey into themselves to give the illusion of an internal skeleton and bilateral symmetry. They are described an having "elemental heritage" that was "corrupted by the powers of chaos," whatever that means in this context.
Where fantasy gaming has failed in my opinion is that slimes have generally been repetitive to the point of banality. Slime Rancher is like a breath of fresh air because it gives more creative designs and powers to its slimes. Rock slimes roll around in their spiky exteriors, quantum slimes teleport, dervish slimes generate tornadoes, etc. I wish slimes in fantasy gaming were that creative more often.
I forgot to mention it in my last post, but the Monster Encyclopaedia book by Mongoose Publishing included a "primordial ooze" monster. It had a trait similar to the chaos beast in that those struck by its attacks risked degenerating into pools of primordial ooze themselves. A second trait allowed it to sacrifice hit points to spawn an entirely different monster like a beast or a giant, a nod to the origin of its name.
Then we have the intelligent (and sometimes humanoid!) slimes. Jubilex, the lord of slimes and poison is the foremost example. More recently we have been introduced to humanoid-presenting slimes in anime, such as Jellax from Sailor Moon and Rimuru Tempest from That Time I Got Reincarnated as a Slime.
- Jellax was a simple amorphous slime monster that could reshape itself into various weapons. It apparently proved so popular that somebody wrote a fanfic where it tries to conquer Earth.
- Rimuru was a human reincarnated as a slime with the ability to replicate the properties of substances he consumed, effectively making him a shapeshifter. Instead of going the evil overlord route, he decided to become a benevolent dictator over the monsters of the forest he lived in.
- Jubilex (aka Juiblex, Ghaunadaur) is not a very detailed or important figure in fantasy gaming at large, tho I like to tweak him into the god (not simply a random demon lord) of slimes and poison elementals. (Yes, I treat poison as an element.) I even conflate him with Abhoth from the Cthulhu mythos.
I hope to explore more in the future. That's all for today!