'Include' means 'to count (someone/something) along with others':
- We were sixteen for dinner including the children.
- Up to and including the 31st December.
- Did you include Aunt Mabel among the people you have invited?
'Contain' has the sense of 'hold':
- This box contains two pounds of chocolates.
- The bottle contains one litre.
'Contain' can also have the meaning of 'hold back' or 'restrain':
- She could hardly contain her fury.