Welding uses a torch to melt the pieces at the joint that you are fusing together (no external alloy or material added as a joining agent).
Soldering uses a soldering iron (like a probe) and and a low-melting point alloy (called a solder) to join two pieces together.
Brazing is a type of soldering, specifically using an alloy/solder of copper and zinc at high temperature, usually associated with joining pipes.
And yes, solder is pronounced like "sodder" (the 'l' is silent).