Is it possible for two different compounds to be made from the exact same two elements? why or why not? with a limited number of elements (less than 120 are known), does this mean we also have a small number of compounds or do we have a large number of compounds in this world?

There are millions of compounds possible. They come in all sorts shapes and sizes and if you throw oxygen into the mix you can get many more. The hydrocarbons are the most common (and I might say the most used - mostly for fuels) of the Carbon Hydrogen pair of elements. That is likely the answer to the question you have asked.

Methane is CH4

Methyl Alcohol is a very common derivative (CH3OH). This stuff has many uses. Right now those of us living in what can be severe winter conditions might put this in our gas tanks. It absorbs water which can be really deadly in winter.

C8H18 is Octane. Your car won't leave home without it.

But there are other pairs that are possible

NaCl     is ordinary table salt. Try living without that.

NaClO

NaClO2

NaClO3

NaClO4

The list and combinations is quite extensive. If you knew everything there was to know about the Periodic Table and how it combines its members you would be a very wise chemistry student indeed.