What size/kind of boat does this actually refer to? "Sailboat" sounds made-up to me - or maybe it's from a dialect that I'm not familiar with. UK here. A yacht? Or is it a generic term for any boat with a sail that I don't have a word for in my dialect of English?
I think in England we would use yacht or sailing dinghy rather than sailboat ( sounds like a child's toy)
I took it to be an Americanism, like: "airplane". Although I understand what a "sailboat" is, it's not a term I'd ever use myself. I think here (UK) we'd be more likely to say: "a sailING boat" - and I'm pleased to say that was accepted as correct. I didn't try: "yacht", as I thought that might be pushing my luck too far.
The Dutch for "yacht" is "jacht". In fact, according to Wiki (not the most authoritative source, I'll be the first to admit), the word entered the English Language from the Dutch: https://en.wikipedia.org/wiki/Yacht
The Dutch pronunciation of 'j' becoming a 'y' in English.
'Yacht' is still not accepted. I think it should be; while 'yacht' can also mean 'luxury small ship' (like the things in Monaco harbour) - as apparently can 'jacht' as per your comment below - the general meaning of it is 'small sailing boat used for pleasure' which as I understand it is close to the meaning here.
A fishing boat with a sail would presumably be a 'zeilboot' and not a 'jacht' (or 'yacht' in English), but those are so rare as to not be relevant to the conversation imo.
In American English, a sailboat is a boat with sails which is usually smaller than a yacht. You can rent a sailboat that can be managed by 1-6 people (depending on how big the boat is) at many lakes. A little toy boat like the photograph in another comment is also a sailboat.
In my mind, a sailboat is smaller than a yacht is smaller than a ship, even if they all have sails. (Though only old-fashioned ships have sails.)
When do you say "sailing vessel" (not accepted) and when "sailing ship"?
I would hardly ever say "sailing vessel", and certainly not in ordinary everyday conversation, when describing something I want, or have seen. It sounds excessively formal and pretentious. Perhaps if I were writing some kind of academic paper, I might say: "In 1850 the fleet comprised some 80 sailing vessels" (I'm totally making these figures up), but even in that context, it would be perfectly adequate to say: "ship", and you don't really need to substitute: "sailing vessel", unless your writing is getting a bit repetitive, and you're desperately searching for an alternative phrase, to avoid using: "ship" for the twelfth time, and make it sound as if you're someone who has a wider vocabulary at their disposal.
I would certainly understand if someone told me they wanted a sailing vessel, but would assume they were either not a native English speaker, or a bit eccentric.
I suppose it might appear in formal legal documents, too, but definitely not everyday conversation.
As an aside, "ship" is usually large, "boat" small. So If somebody said they wanted a ship, I'd assume they were very rich, if they said a boat, I would assume something more modest (although you can have very luxurious and expensive boats, of course).