A composite is an image composed of other images, often, but not always integrated to look like a single image. The term and process are routinely used in the arts, graphic design and film-making. Remember David Hockney's [Link] "Joiners" ? They were images composed of scores (or hundreds) of 4x6" prints, possibly the most famous of which was "Pearblossom Highway". [Link]. That's a perfect example of an analog composite in photography.
Today we see mostly digital composites in movies, graphic designs and art. A good example is in the currently in demand photographic work of the Russian artists who collectively go by the name "AES+F". Here is one of their digital composites [Link] from Sotheby's Institute of Art, London. Others....[Link], [Link] (one of nine panels). Their work also includes single imagery & sculpture. For those interested, prices run from $8K USD to $30K+ USD. One other well-known artist who uses digital compositing is Andreas Gursky. [Link], [Link], one of whose works has sold for over a million USD.
It is a frequent and mistaken notion that compositing, in digital or analog form says anything about the source of the component imagery. It does not. They can all be from one source, say, the artist, or from many sources. It is also a mistake to think that this is a new idea because of Photo Shop. Compositing has a long tradition in movies and photography, and was in use by many artists in the mid-1800's. The most historically famous example of which is this: [Link],
Ps. Note that a composite made up of images done at the same time, like Hockney's analog "Pearblossom Highway" has a very natural look, with directional light and corresponding shadows. Turn to a composite done from many, many images, and maintaining the illusion of coherent illumination becomes exponentially difficult, if not impossible. Most artists take the path of least resistance by resorting to tweaking the collage components into a surreal "shadowless" non-directional lighting. See the AES + F links above, and the Rejlander example. This is one way to tell, although one should be very careful with assumptions like this. There's at least a couple of photographers who actually photograph very complex images, involving dozens of people, in a studio, using soft lighting that looks like a composite, but is not.
Also some (like Gursky) shoot every component of composites under the same light (usually artificial) to retain the illusion of coherence.