Forms of Solder
By form I am referring to the physical nature of the solder or basically how it is packaged.
Sheet: As the name indicates, this comes in a small sheet It is usually very thin and only a few inches wide. To cut it, you use scissors to cut small rows across and then cut tiny pieces off the rows. Try only cutting what you need so that your solder stays clean.
Wire: Much like the row of sheet you cut above, this comes in a wire roll rather than a sheet. It is handy for those who prefer to not to cut the solder (though you can do this of course) and would rather use it like a stick, pointing it to the area you plan to solder at the same time while holding the torch in the other hand.
Paste: Paste solder typically comes in a syringe so you can point to your soldered spot and squeeze out a little on it. It is also available in jars as well, and often you can get it with the flux already in it (which normally you put on the metal before the solder to help clean and keep your solder in place).
Alloys of Solder
Alloys refers to the metals that the solder is available in, and pretty much just like there are different types of metal (silver, yellow gold, white gold, etc.) there are also different alloys of solder. What you use depends on the type of metal you solder and the temperature required to melt the solder. Below are some of the most common silver solders.
Hard: Melts at 1425F or 773C.
Medium Solder: Melts at 1390F or 747C.
Easy Solder: Melts at 1270F or 711C.
Easy Flo Solder: Melts at 1270F or 681C.
The average silversmith will find they use hard, medium, and easy (also known as soft).These types of solder are used depending on the melting temperature (high to low) and are used best when a piece is soldered more than once. For example, if you have to solder a piece three times you would start with hard, then use medium for the second solder, and finish up with soft for the third solder.