An emulsion is a suspension of globules of one liquid, (e.g. latex or vinyl), within another, (e.g. water), where the two liquids normally don't mix. When applied to a surface, the water evaporates and the globules join together and adhere to the surface.
With oil or resin based paint, colour is mixed into the oil or resin which then evaporates to form a finished surface. Evaporation can be slow, so additives called 'dryers' are used to help speed up the process.
Emulsions tend to be much less hard-wearing than oil based paints, so are more suitable for surfaces like walls and ceilings that are not subject to wear or contact, .
Oil based paints are harder, and would normally be used where there is more chance of wear or contact, like doors and their surrounds, windows, skirtings etc. But you might also see it used in hallways below a dado rail, where persons clothes could rub against the wall.
Most emulsions don't take kindly to being washed, while oil or resin based paints aren't affected.
You can certainly apply oil based paints to wallpapers and anaglypta, but think twice. Removing the paper later can be sheer murder, since you've given it a hard waterproof surface that won't soak off.