I would argue that (in the U.S. at least) there is an obvious and well-understood distinction between, "owning a multi-family home" (as the OP phrased it) and, "owning a unit in a multi-family home." The former is widely understood to mean ownership of the entire building (in every city I've lived in where two-, three-, and four-flats are common).

These kinds of buildings are not priced much higher (if at all) than single-family homes and owner-occupied arrangements (meaning the owner of the entire building occupies one unit in the building) are extremely common.