You are correct, yes, Big Ben is the bell. However, people typically class the tower as Big Ben even though it is actually called as you rightly say Elizabeth Tower.

The tower is a four-sided clock design rather than a bell design, which would see the bell visible from the outside.

But thanks for the comment, as the point could easily be misinterpreted by those who interpret Big Ben to mean the bell! I will clarify the point so as to avoid confusion!

Thanks for reading, and for commenting! Much appreciated :-)