I've always used "faltar" to mean "to lack, to be missing".
But in my reading I find that "carecer" seems to mean exactly the same.
When should I use the one or the other? Are there some differences?
They mean almost the same
Now, carecer its used followed by the preposition de so if you want to say (i.e.) I don't have any money, you just say:
Saying that is like saying that you don't have it AT ALL.
Now, faltar is reflexive:
Now, if you say
It doesn't mean you don't have it at all, It means you have some but not the amount you need or want.
There is a subtle difference between the two. Allow me to explain:
Faltar is indeed when something is missing. "Me falta tiempo" I lack the time
Carecer is rather something that you never had. Something you don't have. Sort of. For instance: "Rodrigo carece de paciencia" Rodrigo has a lack of patience || Rodrigo has no patience
Here are the definitions:
From Word Reference
You can see that faltar has much more connotations depending on the context. They are very alike. Falta is used too when someone is at fault, whether morally or physically.
Hope this helps!