Personally, I consider space, subspace, hyperspace and realspace to be seperate dimensions, if you will, that overlay one another. All parts of space time, they have different properties and can be used for different things, although it is generally theorised that subspace is an inferior, or low level, version of hyperspace.
In a fictional sense, subspace, hyperspace and realspace are considered to be areas that provide faster than light travel through various means, the most common being that they either a) inhabit different physical laws to their counterparts, and/or b) are on a smaller scale, allowing you to move 5 kilometers to every one (for example).
Subspace is generally accepted as the lowest form of jump space (any spacial dimension that increases travel speed), Hyperspace to be the next greatest and realspace as the final (or at least, densest) level. Each can be accessed to varying degrees, although total immersion within any of the three is likely to result in permanent loss of the object immersed from space itself. Hyperspace and Realspace have greater chances of causing collateral damage, loss of immersed object etc. due to the density of the dimensions they inhabit (and the energy contained therein).
EDIT:
It helps if you think of the four layers as a ball, with space on the outside, then subspace, hyperspace and realspace in the core. It's obvious that burrowing through the areas closer to the core will get you to the other side faster than walking the whole outside, but the difficulty in burrowing and the likelyhood of cave-ins increases as you get deeper.