I wanted to know the difference between Great Old Ones and Elder Evils. 5e makes little mention of Elder Evils, and it SEEMS like they are the same thing (just renamed).

The player's handbook describes Great Old Ones as...

a mysterious entity whose nature is utterly foreign to the fabric o f reality. It might come from the Far Realm, the space beyond reality, or it could be one of the elder gods known only in legends. Its motives are incomprehensible to mortals, and its knowledge so immense and ancient...

...and lists some deities such as Ghaunadar, and Tharizdun. But also lists non-deities (but POWERFUL entities) Dendar, Zargon, and Cthulhu;

Meanwhile, the 3.5 book "Elder Evils" says the Elder Evils are ...

Buried in the deepest bowels of the Underdark, hidden in the farthest reaches of the multiverse, or lost in the gulfs between realities are terrible things that exist only to destroy or horribly remake creation. So mighty are these ancient beings that even the gods think twice about standing against them. 

... and it includes Zargon (listed as a "Great Old One" in the PHB). I'd think Cthulhu would have been listed in this book as well (but something tells me there would have been copyright issues if they detailed him completely).

And then there are star spawn, far realm infested stars, and aboleth elder evils. This site (https://forgottenrealms.fandom.com/wiki/Elder_evil) lists a few categories, but has no mention of "Great Old Ones". 

Thoughts?

For clarification, I believe you mean specifically for Faerun/Forgotten Realms, and not just in general?

I believe GOOs are a type of elder evil, but there can be elder evils that aren't GOOs.

For clarification, I believe you mean specifically for Faerun/Forgotten Realms, and not just in general?

Um... probably both. How they fit into those realms, but also generally.  :)

There is clearly difference in the lore between the two editions, it wouldn't be the first nor the last time that a 5e book reframes something from previous editions, for example, the 5e rescued the difference between The Elder Elemental Evil and Tharizdun, which were seen as the same entity in 3e and 4e, but are different entities in all other editions.

That said, let's get to your question. It seems to me, at least for now, that currently they no longer refer to Elder Evils, even the Elder Elemental, which was understood as an Elder Evil, is only referred to as the Elder Elemental EYE, so I can't say if they have abandoned the term Elder Evil by Great Old One or if they will still present Elder Evils as another type of entity in the future.

PS: The Great Cthulhu and all of Lovecraft's work is currently public license, there is no contract or restriction that prevents anyone from using it as part of their work.

Quote from Jabbamonkey >>

For clarification, I believe you mean specifically for Faerun/Forgotten Realms, and not just in general?

Um... probably both. How they fit into those realms, but also generally.  :)

I can't speak to FR, as I don't use it.

However, in terms of The Great Old Ones...

Depending on how broadly you go (some folks stick to just old HP, others add in August Derleth and/or the HP circle, still others include all the "popular" additions) you got upwards of 300 different entities to deal with.

They can broadly be grouped in to five rough appearance categories: Blobs, Tentacles, Gloops, Arachnids, and Crustaceans. There are exceptions, but the key thing is that they are all very much intended to give you the willies, and, ultimately, after a short exposure, drive you to madness. 

Derleth did most of the major work, including the formalization of the Great Old Ones (from notes of HPL's) and creating most of their opposites the Elder Gods. HE did a lot more, but there are arguments among purists and others.

For the most part, be aware that Chthulu is one of a dozen or so really potent powers that are all asleep or trapped in a dimension just off our own, and that all people like humans (so pretty much all life on a given planet) matters less than ants do to us.

At least in the fiction, lol.

In D&D, going back to the original publication of Deities and Demigods, they have been pretty much normal gods or slightly more than normal gods, whose influence slightly mirrors the above, mostly in their grotesque appearances and their madness inducing aspects. If you use them, I suggest you use the madness rules in the DMG.

For the most part, they don't really do much. It takes enormous power to get their attention, so most folks make deals with one of the Old Ones (a lesser category) in search of power, never realizing that they are being used and tricked and manipulated into giving the Old One more power so that *it* can bring through one of the Great Old Ones and destroy the world.

In terms of how they show up in your campaign, totally up to you. I use them as a vague background force that has no day to day application but can be a topic of mention or role playing. Like the traditional PIE Deities, I have them as Vestiges, almost powerless, and twisted and warped into unrecognizable, madness inducing forms. If a warlock in my world tried to take one as a patron, they would likely succeed and be utterly unplayable because they would have no rational thought left.  That kind of thing.

In a fellow DMs game, they have a list of over 300 (including some they created) that is growing slowly, and those are all more traditional, derleth influenced or inspired versions and the Elder gods represent the "good", the Great Old Ones represent the "Evil", and the PIE gods (greek style) represent Order and Chaos (in the form of the Titans).

So however you want to use them is good. 

The wikipedia stuff isn't terrible when it comes to this, so definitely use that.

One possible reading is that “Great Old One” is being used as a class of Warlock patrons that broadly overlaps with but not identical to the Elder Evils, similarly to how the “Fathomless” patron is one of a variety of powerful oceanic entities.