Welding, brazing, and soldering are all methods for joining two or more pieces of metal. The key difference among these processes is the temperature used to create the joint. Diffusion bonding is a more modern technique involving heat but no filler material.
Welding
The two pieces of metal are melted to create a consolidated joint. Welding may or may not involve the use of filler metals or shielding gases.
Welding is becoming increasingly popular with TIG (tungsten inert gas), electrical resistance (tack or spot) welding, or laser.
Brazing and Soldering
Filler metal is melted between the two materials, but the two pieces of metal are not.
The liquid filler metal wets the base materials through capillary action. When the liquid filler metal solidifies, it is bonded to the base materials, creating a joint.
Brazing is a higher temperature equivalent of soldering. The cut-off temperature is 450˚C/840˚F.
Bonding
Heat and pressure are applied to the metals being joined, but no melting occurs if we are joining dissimilar metals.
This is used in Mokume Gane.
Cover Photo of a Pulse Arc Welder. Source: The Bench by Cookson Gold