Oxy-fuel welding (commonly called oxyacetylene welding or oxy welding or in the U.S. gas welding) and Oxy-fuel cutting are processes that use fuel gases and oxygen to either weld or cut metals.
There are a few differences between the two. In Oxy-fuel welding, a welding torch is used to weld metals. In Oxy-fuel cutting, a cutting torch is used to heat up ferrous metal to kindling temperature (about 980¢XC). A stream of pure oxygen is trained on the hot metal which chemically combines with the iron which then flows out of the cut, or kerf, as an iron-oxide slag .
Torches that do not mix pure oxygen with the fuel inside the torch, but burn it with atmospheric air, are not oxy-fuel torches and can be identified by their single tank. (Oxy-fuel welding/cutting needs two tanks, fuel and oxygen.) Most metals cannot be melted with such single-tank torches, so they can only be used for soldering and brazing, not welding.
Note: Sometimes a metal-cutting torch is colloquially called a "gas-axe", "smoke wrench", "hot wrench", "blue wrench" or "hot blue spanner" (in Britain). Colloquially, many people mistakenly call a welding torch a blowtorch. In the USA the word blowtorch is also used for what in Britain is called a blowlamp.