With many years experience making surgical instruments may I offer?:
TIG welding is the most versatile, but the machines cost a lot of money, and training. The range of possible size of the objects to be welded are truly astounding, and the control of the welding process is almost unequaled. It is the most suited to gunsmithing.
“Silver-soldering”, as usually cited, can be either “silver brazing”, when the temps are above 800 degrees, and (properly) “silver-soldering” when the temps are less than 800 degrees. “Silver-brazing” is much stronger, but more likely to affect the strength of the parent metals, because the temps are higher. “Silver-brazing” is weaker than any type of welding, but easier to perform, and will less-likely affect the parent metals, especially if a “low-temp” silver solder is chosen. Either torches or induction-heating can be used. “Silver-soldering” is stronger than lead-tin soldering, and used to be how double-barrel shotguns (etc.) were made. Some “silver-solders” will melt around 450 degrees.
Shielded-Metal-Arc-Welding (SMAW) is the full technical term of “stick-welding”, when one uses an inexpensive “arc-welder” to do general-purose welding. This is the least-appropriate form of welding for firearms, unless one is simply making tools for gunsmithing.
MIG welding is Metal Inert Gas Welding, where one uses a special coated wire (from a coil) in a special MIG machine. It is somewhat like SMAW, except that the wires can be very much smaller, easier to control (even with foot-pedal-controlled wire feeding), and one can weld quite small objects. Costs for the machines is in between the TIG and SMAW types. Some gunsmithing applications exist.
Torch-welding requires a lot of practice and experience to do correctly, and can never equal the quality of either TIG or MIG, because of the temperatures used with an unshielded workpiece. The parent metals are unavoidably degraded by atmospheric oxygen. The only gunsmithing applications should be for making tools, or non-highly-stressed parts, like locks for black powder firearms.