Maybe the term „train station“ is ambiguous, but I would argue that „rail station“ is the generally accepted term to cover intercity and suburban rail stations without including stations which only serve urban rail services such as Metro, LRT or Streetcar.
May I ask you how many „rail stations“ Ottawa, Toronto, Montreal, Vancouver, Amsterdam or Frankfurt have according to your personal definition? If someone asks you in downtown Toronto where the „rail station“ is, do you point them towards the nearest streetcar stop or Union Station?
Correct, and Ottawa seems to be a very notable and extraordinary exception.
Correct, if a station has a particular name, the transit station will adopt it and where it doesn’t (like in Ottawa) it wouldn‘t and just generically refer to it as something like „rail station“.
Correct, Ottawa‘s VIA Rail station does not have an alternative name and it doesn’t need one, because it clearly is the highest-order station serving the city.
Incorrect, given that there is only one rail station named after the city, there is no need to designate a name to that station. My favorite example is Leeds (where I did my undergrad), which has
15 rail stations within the city proper, but only one station called „Leeds“, which is served by bus stops called „Station“ without causing any confusion woth the other 14 rail stations in the city or the bus station (which is called, well, „Bus Station“):
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Fully agreed.
I‘m not saying that the City of Ottawa (including, but not limited to: OC Transpo) do nothing to serve the VIA station, but I do maintain that they treat intermodality with intercity passengers at the city‘s second-busiest intercity passenger facility (assuming that only YOW airport is busier, since there is no longer a centralized intercity bus station) as an afterthought.
As
@lrt's friend has alluded to, LRT station naming is motivated by many things, but not logic, international conventions or any regards for tourists unfamiliar with the city. For a capital city of a major country, this is a rather pathetic attitude…