To the casual observer these are all grassy type plants but there are differences. Rushes usually have round stems in cross section, also their flowers are in clusters either at the tip of the stem or what looks to be on the side of the stem.
Wood-rushes have flat grass like leaves but often with fine long white hairs.
Sedges also have grass like leaves except that the stem that holds the flowers is normally triangular in cross section. Also they have separate male and female flowers, both on the same stem but looking quite different.
Grasses are very varied and are a huge group, and can be quite difficult. I have always struggled with them. I know some of the main ones but some of the more obscure ones I do find difficult.
They are quite similar and easily mistaken for being the same, they also grow close to each other and seem to like the same conditions, ie damp poorly drained areas. in winter they are often seen on the edge of areas of standing water.
Apart from this they are quite similar, Soft rush can grow a bit bigger and the leaves are smooth or just vaguely ridged, whereas the Compact rush will only grow up to about 100cm and its leaves are somewhat ridged.
So there you have it, look out for a tussocky grass that has leaves that are circular in cross-section, like a drinking straw and then you have identified a Rush not a grass.
One common Rush is called Jointed rush and that can easily be identified because if you squeeze the leaf and run your fingers along the leaf you will feel little joints all the way along. Another rush is called Hard rush and if you squeeze the leaves of this one you will find they are quite hard and resistant and not at all easy to squeeze flat.