What we call "soft" solder is any filler metal that melts below 840 f, and below the solid state of the metal you are soldering.
We say "soft" solder and "hard" solder, but really it's either soldering, as defined above or it's brazing, (sometimes called silver brazing, and what we call hard soldering), which is joining metals with a filler metal that melts above 840 f, and, that does not melt the parent metal.
If a process melts the parent metal to join two metals, it's called welding.
Those are the basics, anyway.
You can get all kinds of soft solder, acid or rosin core fluxed, or solid solder that has to be used with a separate flux. It can be made from any number of different metals. Lead, zinc, tin, silver, and other stuff, usually a mixture of two or more metals, but there are some that are just one metal.
Dean