I've noticed that the different courses I'm using to study have a lot of different interpretations of "Céard atá ort?"

Duolingo thinks it means "What's up?"

DCU/FutureLearn thinks it means "What's wrong with you?"

Google results seem to be pretty evenly split, too.

What does it mean to you--and if it's both, what makes a difference--just context?

It means literally "What is on you?", less literally "What have you?"

There can be a lot "on you".
Often bad things are supposed to be "on you" (worry, anger, diseases), so "What is wrong with you?"

But it always depends on context what is meant.
It can even mean "What do you wear?" (e.g. in case of phone calls).

Edit:
I was told by an English gentleman that "What's up?" means "What's wrong with you?" in British English.
Only in American English "What's up?" is used in a wider sense & as a kind of greeting.