What is the difference between a prime number and relatively prime numbers?

Prime numbers are those which are divisible only by 1 and the number itself...

Example: 7 is divisible by no number other than 7 and 1.

Relatively prime numbers are those pairs of numbers which have no common divisor other than one.

Example:

(15,16)

Factors of 15:1,3,5,15

Factors of 16:1,4,16

Common factor of 15 & 16 is 1, hence 15 & 16 are relatively prime.