May I try to make it simple?
Modern welding involves actually melting the base metal. Almost always, you add a little filler metal (the weld rod) which also melts and fills in the gap.
Brazing and soldering are both pretty much like gluing the joint, except some metal is used for the glue.
For our gunsmithing discussion that braze filler metal is usually either a copper alloy or a silver alloy (when Pratt & Whitney or General Electric build jet engines they use a fancier "braze" metal which has neither copper nor silver in it)
The main difference between soldering and brazing is the temperature at which it is done. You gotta pick some temperature for the definition, and as Tallbear said, the American Welding Society picked 840F (450C)
Until recent decades when people began to fear lead, solder was usually some mixture of lead and tin. The lowest melting point lead-tin solder is 60% tin and 40% lead. Then if you want something that melts a little higher, there are solders which are mostly tin, like maybe 98% tin, with a couple percent of silver in them, or else a little antimony.
The strength of a solder joint, as well as a braze joint too, depends not only on what "glue" or filer metal you used, but also how tight was the joint. A gap of any size makes it weaker. A very tight fit, maybe even a press fit, and the joint will be much stronger. You really don't need to allow any space for that filler metal, it will suck into a very tight joint by capillary action. A thin solder (or braze) joint is stronger than is the solder itself. The reason is mechanical, nothing to do with the metal alloying into the base metal. That alloying will not happen when soldering steel. I personally do not know whether solder alloys with copper or brass base metal to any significant amount.
Now for brazing. We call it "brazing" because for the last several thousand years some variety of "brass" was melted in to make the joint.
Brazing may also be done with just plain copper metal. I have a 16th century Italian wheel lock (lock only, sadly) with a copper brazed joint in it. The torque converter in your favorite Hupmobile is made out of mild steel sheet pieces which have been copper brazed together at a process temperature of about 2050F (1120C).
Silver brazing uses, obviously, a braze metal based on silver. Some copper, tin and other alloying elements are added to get the melting pont you want. In whatever state you dwell I would not suggest breathing cadmium. The good news, of course, is that it may just cause a quick heart attack rather than slow nasty cancer.
Silver braze is not going to alloy into any steel part that you braze.
But if you are brazing copper or brass parts together then some mixing may happen, as has been discussed above.Those alloying additions such as tin, etc, that lower the braze meltling point may diffuse into the base metal a little bit. This leaves the finished braze joint with a higher melting point than originally.
There is also something called "braze welding", where the braze rod is used in a welding machine and the steel base metal may well also melt, as an earlier note discussed with respect to autobody repair. I doubt that you are going to use braze welding techniques in gun building.
MODERN welding involves melting the base metal. Old fashioned FORGE WELDING, by which gun barrels blanks used to be made, does not involve melting at all.
I have some experience with these processes, having had to deal with them as a metallurgist since Kennedy was pres.
