<<"I would appreciate a definition of what a funicular is vs. a cogwheel
train. I think I have the gondola vs. cable car distinction but I could
be wrong on that too.">>
It is easy to get the variations confused. Even more so because "cable car" is an ill-defined name. Many things...such as gondola cars, but also chairlifts, are technically cable cars. I tend to use the term "cableways" ( also poorly defined) when I discuss the things that go through the air on cables.
In part, that is because we have "cable cars" in the USA that are very different. See below.
A cogwheel train ( also rack train) is a train which runs on regular tracks, but which, when steep grades demand it, engages a toothed (cogged) gear wheel (cog wheel)under the locomotive with a third (toothed) rail ( the rack) in the center of the roadbed. In German - "die Zahnradbahn" ( the toothed wheel train). Motive power is provided by the locomotive. Such trains usually can run on regular tracks which do not have a rack., and may have several cars.
In the 'States...Mt Washington:
is a cog-wheel train.
Examples in Switzerland - Pilatusbahn, Rigibahn, and others as shown in the attachments. There are different designs for the gear system, which have names, such as the Riggenbach design.
Since they are powered by the locomotive, they are not limited in length/distance or time of ride. The gearing may be retracted or engaged, as needed.
A funicular is a also railway, running on the ground - usually with only a few cars powered by a cable attached to it/them. The cable in older designs runs over a powered wheel or large pulley at the top, and has two train sets (groups of cars). One is at each end of the long cable. The weights of the cars roughly counterbalance each other, and one comes up as the other goes down. Inherent in the design is the length of the cable. There is no locomotive, so the train cannot operate anywhere but on its specific set of tracks. The old design was developed when power sources where not so strong, and needed needed to have the car weights roughly counterbalance. Modern designs or retrofits can have a sufficiently powerful motors turning that pulley that only one section of cable is needed. So, in that case, the car(s) is(are) on the end of one long cable which winds up and pulls the car up the hill, on rails (so it is a railroad) and holds it back while unwinding as it descends. A mechanism to catch the cars is needed, in case the cable breaks. So, there may be some kind of third rail with teeth that can engage a ratchet under the cars to grab them, if the cable breaks.
I have attached a few images of the Treib-Seelisberg Bahn.
They show a couple of characteristics. The up car and the down car meet somewhere half way up the hill. Since there is only one track most of the way, when the cars pass each other, there must be two tracks. Shown in "meet.." Not needed for the new design with only one car or group of cars on the end of one long cable.
That image also shows the cables running on pulleys in the center of the roadbed, between the two tracks. In that image, the pulleys are tilted where the car is on a curved section of track.
Funiculars are common in mountainous cities, as well as other places through out Switzerland.
Many kinds of cableways go above the ground. There are specific names for each kind.
The "cable cars" in San Francisco operate with a continuously running cable under the train in the ground. The cars themselves have "shoes" that grab the cable to go along with it, or release the cable when they are stopped at a station.
Need more?...look up the names in Wiki.
PS -I'm having some problems with image uploading at the moment, but I'll put some up as soon as I can.