Derek C. said:
is there a difference between the door itself and the gap you actually get
Derek, let me answer the blunt version first: a place that will happily type the word accessible but will not put a single measurement in writing is giving you a real answer, and nine times out of ten that answer is no. The good ones send numbers, or send someone to go and measure. So trust your instinct here.
Now the vocabulary, because it will make you much harder to fob off. The number that matters is not the size of the door, it is the clear opening, which is the actual gap you get when the door is open flat against the frame. The door leaf is always a few centimetres wider than the clear opening once you lose the hinge and the door thickness, often 4 to 5 cm, so if someone quotes you the door size, gently ask for the clear opening instead. A fairly standard manual chair sits around 60 to 70 cm across the wheels, and most people find they want a clear opening of about 80 cm to get through without barking their knuckles, with 75 cm the tight end where you are folding your elbows in. Powered chairs and scooters run wider again. Inside the bathroom the second number is turning space: to spin a chair round you want something close to a 150 cm clear circle, and a lot of "accessible" bathrooms are really a standard room with a grab rail screwed on and nowhere near that.
On the shower, this is where Brenda got caught and it is worth being precise. Level access, sometimes written roll-in, means the floor runs flat straight into the showering area with no lip at all. A wet room is not automatically that: plenty of wet rooms have a small upstand or threshold of 2 to 4 cm to keep the water in, and even that low a lip can stop a shower chair or a small front castor dead. So ask specifically, is the shower level with the bathroom floor or is there a lip, and how many centimetres. While you are at it ask the bed height, because a lateral transfer is far easier when the bed roughly matches your chair seat height rather than towering over it. The full list I paste for exactly this is in the questions to ask before booking, and the wider picture of what separates a real accessible room from a hopeful one is in accessible accommodation.
Two honest exceptions so I am not painting every hotel as dodging you. Some genuinely good places have front desk staff who simply do not know the numbers off the top of their heads; the fix there is to ask them to have maintenance or housekeeping measure it, and the willing ones will. And in older or historic buildings you sometimes find a portable ramp kept behind reception for a threshold, which can turn a no into a yes, so it is worth asking whether one exists rather than assuming.
Where I stop: what clear opening YOUR chair actually needs, what threshold height you personally can manage, and whether a given transfer is safe for your body are not things I can size for you from here. Those belong to your own OT or physio, who know your chair and your transfers. I can tell you which numbers to demand. What those numbers mean for you is theirs to judge.