By definition: Plex - def #2 a building divided into a number of spaces (like duplex, movie plex, multi-plex). having # apartments, divisions or floors.
From the Glossory of Real Estate Terms:
Duplex, Triplex, Quadraplex - These multi-family housing terms simply define the number of units contained in a multi-family building. A duplex consists of two units per building; a triplex, three units per building; and a quadraplex, four units per building. While the duplex and triplex are generally built side-by-side in a row, the units in a quadraplex are generally constructed back-to-back.
Townhome/Townhouse - The term townhome-or townhouse-originated in the United Kingdom and simply denoted exactly what it was - a home in town. The townhome was generally owned by a peer or member of the aristocracy, as an alternative residence to their country home, to be used when parliament was in session. The original townhouse units were attached side-by-side in a row creating the illusion of one massive building. Many have since been converted to tenements, aka rental apartments. Thanks to its urban roots, the design of the townhouse remains distinct, being relatively narrow, tall (multi-storied) and uniform. This configuration is also known as a "rowhouse." This term is not common in the US as the perception of a rowhouse is that it is smaller and less luxurious than a townhouse. In recent years, the townhouse/townhome has evolved to represent non-uniform units in suburban areas that are designed to provide the perception of a single-family home in spite of the product's inherent "attachment." The units themselves have also grown in size. While the traditional townhouse apartment is defined as a two bedroom unit with the living room in the front on the lower level, the kitchen in the back, and two bedrooms on the front and back of the upper level with a single bathroom between, contemporary designs now include three and four bedrooms, an equal number of bathrooms, and floor plans of great variety. Most modern townhomes also accommodate a one or two car garage.
Multi-Family Housing Products - The multi-family housing category includes many configurations ranging from side-by-side townhomes and villas to high-rise buildings containing an abundance of apartment flats, and various and sundry types in between. Many of the terms used to define a particular multi-family housing product are interchangeable, making their definitions somewhat dubious. What follows represents definitions that are generally accepted by the US building industry. That said, the terms do, vary from region to region and community to community.