Types in MySQL: BigInt(20) vs Int(20)

I was wondering what the difference between `BigInt`, `MediumInt`, and `Int` are... it would seem obvious that they would allow for larger numbers; however, I can make an `Int(20)` or a `BigInt(20)` and that would make seem that it is not necessarily about size. Some insight would be awesome, just kind of curious. I have been using **MySQL** for a while and trying to apply business needs when choosing types, but I never understood this aspect.