Drifting and tunneling are all different methods and approaches utilized in underground drilling and mining to both drill and blast the rock and support the rock.

Drifting refers to the horizontal tunnel that is dug following, for example, an ore vein. It can, however, also be used to describe small exploratory tunnels used to investigate engineering properties of the rock mass. A third use for the word or smaller cuts made to a rock wall that needs to be excavated, which is then expanded out to cover the whole face of the wall with explosives. 

Tunneling, on the other hand, is the general reference to any sort of horizontal excavation of landmass, the goal of which is to produce a tunnel, rather than to dig for minerals. Tunneling can utilize drifting, but also other methods such as forepoling, and is often used for construction purposes.