I think they mean basically the same thing, the difference is merely stylistic. "You're welcome" and "My pleasure" are more suitable in a formal setting, while "Sure" and "No problem" are more informal.
For example,
- Thank you for helping me with this task, Mr. Johnson!
- You're welcome.
or,
- Thank you for helping me with these bags, Mr. Black!
- My pleasure, Ms. Smith.
and,
- Thanks for driving me home, dude.
- Sure.
or,
- Thanks for your help, Jack.
- No problem.
When in doubt use "You're welcome". It's universal.