Are faucets called fixtures?

Yes, faucets are called fixtures, though more precisely they fall under the category of plumbing fixtures or fixture fittings. A faucet (called a "tap" in British English) is the valve mechanism that controls the release of water from a building's supply system, and it is considered part of the fixture assembly because it is plumbed directly into the water supply lines and mounted to a sink, basin, tub, counter, or wall. In plumbing trade catalogs and hardware stores, faucets are stocked and sold in the fixtures and faucet section, and building codes count faucets when calculating fixture-unit loads for water supply and drainage design. A faucet's permanent attachment is what qualifies it: it is connected via threaded supply fittings and shut-off valves to pipes within the property, and removing it requires tools and water shut-off, satisfying the annexation test of fixture status. In everyday and real estate language, however, usage is slightly nuanced: the whole assembly (basin, drain, faucet, and connections) is usually described as the fixture, and the faucet is sometimes called the "fixture trim" or "fitting" because it can be unscrewed and replaced more easily than the basin itself. This is why a seller replacing an expensive designer faucet with a basic model before a sale can be a point of dispute, though legally the faucet connected at the time of sale is generally included. So the accurate answer is yes: faucets are fixtures in plumbing terminology and are treated as part of the plumbing fixtures in codes and in property transactions, with the minor caveat that they are sometimes specifically called fittings or trim.