Silver solder is used to attach pieces of sterling silver together when making jewelry. It comes in different alloys, referred to as hard, medium and soft. The softer contains more non-silver, so it will melt at a lower temperature, but the silver content is still high.
This silver solder comes in either wire form, or small thin sheets which the jewelry maker cuts with small shears into tiny squares or other shapes for use.
Fine silver can be used as hard solder, because it melts at a lower temperature than sterling. Some bezel strips are fine silver, because it is softer than sterling, and can be rolled over the stone easier. But a medium silver solder needs to be used or the bezel will melt when soldering it to the back plate.
Medium silver solder will present a slightly darker color than the sterling. The soft will be noticably darker, and is only used if it can be hidden. Soft is necessary only if soldering near another solder connection of medium hardness, so as not to remelt that connection.
But all of the silver solder grades have a high silver content, so it won't degrade the overall silver content of the jewelry piece too much.
The 60/40 ratio is the old common electronics solder ratio of tin/lead, before everyone realized how dangerous the fumes were, and that it shouldn't get into land fills. Silver electronics solder has the much smaller amounts of silver, and a much lower melting point.
I don't know what the brazing silver alloy is.