Difference between internal and external modem?

An internal modem is going to be one which fits into a PCI or other expansion slot on your computer and thus communicates directly with the BUS on your motherboard.

An external modem connects to a computer via a serial port, parallel port or USB port. This means it will need to go through a controller chip before being allowed access to the main system BUS.

If you are referring to analog modems (aka, dial up) then the difference will be very little. It is more important to get a "Hardware" modem and not a "Win" modem which uses the CPU of your machine to emulate a controller chip, thus causing it to slow down slightly. Of course on modern PC's this is negligible.

If you mean a modem for DSL or Cable for example most will be external. Usually connected to a router of some kind and then fed to your computer(s) with network cables which would be transparent to the computer.

Hope this helps!