Those are the generally accepted alternate approaches to duplex. Some cities don't even allow those to be called a duplex if it's not over and under and limited to two floors/units, but many cities allow two, three, or four units to be separate floors or to even share floors and have single-floor units (so, four units in a two-story building, two on each floor), so long as each have separate entrances.
Some cities have no restriction of the term, and you get some weird situations where apartment and duplex/quadplex/etc start overlapping.
As you said though, side-by-side is basically the main alternative approach.
It would definitely be my preference to have a side-by-side unit if I'm looking for a duplex.