See subject line. Welding differs fundamentally from brazing and soldering because it involves melting of the parts being joined (in addition to melting of the added filler metal). But what differentiates brazing and soldering from each other?
I think brazing uses brass.
Braising uses brass and the process is slightly different because of the way iron conducts heat as opposed to copper. Braising you need to get the iron red hot and flow the brass into it almost like welding. Solder the temperature of the copper just needs to suffiecient to melt solder.
Explains my wife’s cooking. 
Brazing and soldering are fundamentally the same process. Brazing occurs at higher temperatures than typical “soft” soldering, but there are some silver solders (“hard” solders) which melt at close to brazing temperatures.
At least you had something to eat before she began reading your posts.
You are to be forgiven for asking, because the terms are not consistently used. It is a distinction based on temperature, and the terminology has changed over time, and varies by trade. In all cases, these refer to joining processes where the filler sticks to the base metal, but the base metal is not melted. If the base metal is melted into the joint, it is a welding process.
Hard solder, silver soldering, and silver brazing all refer to similar processes. In some cases, like for bicycle frames, it is just called brazing, even though a silver alloy is used as the filler. This is done at 1100F or a little higher depending on alloy…dull to cherry red heat. These processes are common for bicycle frames and air conditioning trades.
“Brazing” used alone usually refers to using brass or bronze filler, at slightly higher temperature. Cherry red to dull orange heat.
Both of the above produce very strong, mechanically sound joints. The bronze filler is cheaper, but the lower process temperature of the silver based alloys usually results in less damage and warping of the base metal, and also is usable on brass and copper. Sil-phos filler is self fluxing on brass and copper, so this is preferred in the air conditioning trade.
Soldering, soft soldering, tin-lead soldering, tinning, or silver-bearing solder all refer to lower temperature processes with low melting point fillers. They produce fairly weak joints, just strong enough for plumbing with liberal lap joints, and fine for electrical connections not subject to mechanical strain. These are done at well below 1000F.
In some cases, high temperature silver-brazing may just be called soldering if that is typical for the trade. I think this is how Jewlers refer to it.
Brazing usually means hard-soldered, using higher temperature materials. But it’s used interchangeably with soldering, as in soft-soldering, so much that the you never know just by looking at the term. The term silver-solder is often ambiguous also.
Sadly, the hand brazing of bike frames is a bit of a dying art. These days aluminium frames dominate the mass-market with carbon fibre at the high end. Cheapo steel bikes will be robot-welded in huge factories. I’ve not seen a lugged and brazed frame in a long time.
even longer ago cars were soldered (some parts).