Hi Tel,
Plumbing solder in the USA is now basically, Silver Solder. Mostly tin, with a small amount of silver, and no lead. So, when you join copper piping with modern solder you use silver solder and a MAPP cylinder works fine, though Acetylene is hotter, faster and better.
If you are doing precision jewelry-like soldering, I know there are a variety of solders of different composition, different metals too depending on what you are joining. Each has different hardnesses and different melting points. Some comes in premixed paste form with flux added, some in bars, some in strips...
http://www.cooksongold.com/Solders/ Because the melting points vary, you have to choose your tool. A MAPP gas flame is just above 2000 degrees C; the blue propane just below 2000 degrees C; and pure acetylene (without the second bottle of oxygen) about 3000 degrees C.
Since the MAPP and Propane are similar in temperature, my own experience is that the results are similar. I bought a MAPP cylinder/torch once for emergency use and all I did was wish I had the acetylene! It didn't appear to be much better than propane. Some small desktop "systems" will have an oxygen tank too--and that raised the temperature a LOT. I've never used (or needed) such a thing; my experience is limited to propane, MAPP, and pure acetylene in household use. My father and sister have a lot of jewelry experience, however...
Brazing is much like "silver soldering" with a wide variety of brazing materials. You need to know what you are joining in order to select the correct one. For example, to braze copper to copper, you might choose a high silver content (15%) brazing alloy, with copper and phosphorus. Melts well below 1000C. If you are joining steel to steel (or stainless), even higher silver is called for, such as a 40%.
Always best to check with the supplier (or manufacturer) who should be able to help you choose the proper soldering material and appropriate torch/heat source.