If you are using STL fist time , you can see that these are the classes for holding a gropup of things.You need to include #include <vector> and #include <list> for using these classes, also specify they are in std namespace . This can be done by using namespace std;
We all know these stuff. So what is the difference between vector and list ? When i compared the names first time , i can't see any difference, vector is something which has magnitude and direction in maths ( just joking) and list is our linked list ( doubly or single ). No it is not like that , Actually the vector class only allows to insert in the back side or front side ( No addition in between ). But list allows. list has function like insert() , using we can insert to any position. You may think then why we need vector? Ofcourse we need because , list costs perfomance degrade for allowing us to insertion in between the two ends. So IF you don't want to insert in between the front and last end , use vector. This can be speed up your performance.One other difference is in vector each elements can be accesses using  . But in list it won't possible.
These are the Key differece. In implementation wise vector is like dynamic array (When i say dynamic array u may think that "Is that same linked list ???" , Not exactly ,the STL doc says that they have done some perfomance tuning for vector) , and list is the same linke list