First name vs Middle name vs Last name

First name or Given name: 
Both mean the same and it is a personal name given to someone after birth or baptism as the case may be. The person is usually called by this name.

Family name or Last name or Surname: 
Again, all three mean the same and it is the name common to all memebers of a family 

Middle name or Second Name: 
It is an additional name placed before the surname and after the first name. Other members of the family may or may not have the same middle name.

Example:
Jade Lim :
First name or Given name: Jade
Family name or Last name or Surname: Lim

George Bernard Shaw / G. B. Shaw / George B. Shaw :
First name : George 
Family name or Last name or Surname: Shaw 
Middle name or Second Name: Bernard