Wikipedia’s article gives a list of a variety of modes largely defined by their technology (are they powered by animals or engines, are the engines on the vehicle or is the vehicle powered by a cable, do the vehicles travel on land, sea, or water, etc. While this is a reasonably comprehensive list and a reasonable organization of the subject for Wikipedia, it does not really get at the transportation aspect of modes, focusing instead on their mechanical aspects.
What characteristics describe and differentiate modes? Every mode must differ from every other mode on at least one dimension (otherwise they would be the same mode). This is analogous to the idea of speciation in biology. The Figure is a first cut at this for surface passenger transportation.
This distinguishes primarily on the non-mechanical (non-propulsion) characteristics of the service. Of course not every possible dimension is identified, and a few of the circles contain multiple modes which are otherwise obviously distinct (e.g. gondolas and subways are much the same from a transportation service perspective but for one is underground and uses a train and the other is suspended by a cable which moves it). This taxonomy differentiates things that were qualitatively different rather than quantitatively different.
So the first cut is about time, is a reservation required or not (i.e. does it need some advance planning).
The second cut is about time as well, is the service scheduled or dynamic.
The third cut is about space, are the routes fixed or dynamic.
If the route is fixed, are stops fixed (i.e. does the vehicle stop at every stop, or only when called, like a bus).
Otherwise if the routes are dynamic, things get a bit more ad-hoc, as the key question changes.
Some traditional distinctions (access mode vs. primary mode, such as walk to transit vs. drive to transit) are not distinguished here, rather that would be thought of as at least two trips, one where you walk or drive to some place (with the purpose of changing modes), and second where you take some form of transit.