The concert will begin IN fifteen minutes
The concert will begin WITHIN fifteen minutes
Are the same or not?
The concert will begin WITHIN fifteen minutes
Are the same or not?

The concert will begin
The concert will begin IN fifteen minutes
The concert will begin WITHIN fifteen minutes Are the same or not?
"The concert will begin in 15 minutes" means what it means: in 15 minutes, not more, not less (in theory).
"The concert will begin within 15 minutes" means it will begin at most in 15 minutes but may begin earlier. Hope I'm not wrong.
Jeremy is correct, although somebody might say "within 15 minutes" and intend to mean "in 15 minutes".
Consider:
You will repay the loan within five years. You will repay the loan in five years. With the former option, I should get my money back sooner than with the latter option. 