What's the difference between depend on and rely on? Thanks in advance.
which one is used more often and in what situation? Is there other words have the same meaning?

Question

Answer

In general they have the same meaning, and are interchangeable.

In certain specific contexts, 'depend on'  is used, for example, when analysing the relationship between factors in a process or equation :

The amount of heat generated depends on the amount of fuel available for combustion
The rate of interest on your investment will depend on the length of the term for which you invest it
In the equation  y depends on  x cubed