Do they mean the same thing?
1) It is obvious that she is very clever.
2) It is a given that she is very clever.

See a translation

@simba722
There are many times that the two can be used similarly, but the difference in nuance is as follows:

"a given" -> ***a necessary conclusion***
This means that it is information that is either already directly "given"/provided to you, or is information that is given/provided to you by a necessary conclusion based on X;
Example)
"Her IQ is higher than Einstein's, so it is a given that she is intelligent."
"Only students who can pass our extremely rigorous entrance exams can study here, so it is a given that our class grades are higher than the national average."

"Obvious" can also be used for conclusions that are "a given", but in addition, it is used for things that are directly apparent and/or clearly OBSERVABLE.

Example)
Aさん) Is it already after 5PM?
Bさん) It's obviously dark outside, so it's obviously after 5!
or
"Watching her train, she has obviously improved her skills."

I hope that helps!!