Schooling and shoaling are very different things, so many of us use the terms interchangeably. CaliforniaFishKeeper is absolutely correct, the proper term for freshwater fish is shoaling.
Shoaling means the fish must be in a group of their own species. I use the word "must" because it is necessary; when shoaling fish are not in a group, they are under stress, and that weakens the immune system and makes the fish more susceptible to disease and health problems. They can also be more aggressive, or if normally peaceful, turn aggressive--neons that fin nip, etc.
Also, some species have a social structure within their group. Loaches for instance, and angel fish, and discus, are highly structured, and many of the characins and cyprinids to a lesser extent. When these fish are kept singly or in a pair (except when spawning, that is quite different), they do not have that structure which is part of their natural instinct, and again this causes stress.
Shoaling fish may or may not swim around (in what we tend to think of as a "school"), but they need to be in a tank with others of their species whether they swim together or not, just to maintain the inherent structure. Rasbora are super at swimming together, almost constantly. Rummynose tetra are also pretty tight in a group, and cardinals most of the time. I have several species of characins in my two large Amazonian tanks, and it is interesting to sit for a couple hours observing the interaction of fish with their species group. They clearly have signals, sometimes visible, but also chemical. You can read more about this in the introduction to the characins in our fish profile section--second tab from the left in the blue bar at the top. The profile of each fish tells you how many, tank size, suitable companions, and other info on maintaining the species in the best health and condition.