DIY, craft, materials, and such / Metal notes
Common metals and metal alloys
Soldering, brazing, welding
Soldering often refers to soft soldering - for electronics and sometimes craft. For soldering in electronics, see Electronics_project_notes/Common_terms,_useful_basics,_soldering#Soldering.
Such soldering historically often uses a tin-lead mix (melts around 180°C, depending on mix), while newer lead-free solders melt around 220-250°C (depending on mix).
Soldering in metal plumbing requires more heat to work well (for a good part because the pipes around them act as heatsinks), so faster heat delivery in the form of torches (propane, acetylene) are common.
Aluminium and some steel can be soldered using zinc, which may also need higher temperatures.
Brazing seems to be defined mostly as working with fillers with higher (than soldering) melting points, around 420°C or 450°C and higher, depending on who you ask.
As such, hard soldering (often copper/silver) is often technically a form of brazing.
The term welding is often used when, rather than just adding a reasonable filler to the gaps between two metals you're not really changing, you're melting and coalescing the existing metals (and possibly also something else) This is also the reason why, when done correctly, it is typically stronger. (There is still filler, largely because it just helps, e.g. in spreading the heat)
The term usually suggests metals, but is also applied to (thermo)plastics.
Note that this includes weleding in a forge, which is fine for small pieces and softer metals but unwieldy for anything large, or for stronger metals.
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The most recognizable (and least expensive) form of welding is probably arc welding, which groups a number of techniques:
- shielded metal arc welding (SMAW), sometimes stick welding 
- consumable sticks are the electrode
- a variation of GMAW where the electrode is coated with flux, which releases its own shield gas
- making it one of the simplest and most portable variations (no gas bottles) and the easiest to get started with
- Flux(ed)-cored arc welding (FCAW / FCA) 
- similar to SMAW
- Gas metal arc welding (GMAW) 
- the welding gun supplies a consumable electrode, and a shielding gas
- Metal Inert Gas (MIG) or Metal Active Gas (MAG) indicates the choice of shielding gas
- Inert is often argon and helium, and only used for nonferrous welding, such as aluminium
- Active (mixtures of argon, carbon dioxide and oxygen) and are necessary for proper workings on ferrous/steel welding
- flux on the consumable electrodes supplies the protective gas
- Gas tungsten arc (GTAW), a.k.a. Tungsten inert gas (TIG) 
- electrode itself is not consumable, and also feeds the protective gas
- separate filler rods
- harder to do than than GMAW and more expensive, but more controlled, can be stronger, and can handle more materials
- Plasma arc welding (PAW) 
- much like GTAW
- Submerged arc welding (SAW) 
- blocks contaminants by arcing submerged in a layer of granular flux.
- makes sense in industrial settings
- Electroslag welding (ESW) 
- Electrogas welding (EGW) 
Non-arc welding techniques include:
- Gas welding
- often oxyfuel/oxyacetylene 
- Forge welding