Welding is a process where by pieces are joined by melting.  A properly welded joint is as strong as the individual pieces.
When the parts are melted, a filler material is usually added. The heat source may be gas flame, electricity, lasers, electron beam and even friction.
Metals may be cut using similair techniques.

Gas welding is most commonly done with a combination of oxygen and acetylene gas.  Brazing produces a weaker connection. it requires less heat and uses a flux coated brass rod as a filler.
Soldering is similair using lower temperature.

Oxy-acetylene welding remains the most common form of gas welding and requires the use of steel filler rods (often copper coated for corrosion protection).

Flame cutting can also be done using an oxy-acetylene set-up with a cutting torch

Gas welding requires relatively inexpensive equipment and is portable.