Universal Design is based on the idea that products and environments should be designed in a way to make them usable by as many people as possible without adaption. It’s a very big (and important) idea. Visitability, on the other hand, is a very concrete and specific idea: houses should have a barrier-free entrance and an accessible bathroom.
There’s a wide variation in what people mean when they throw around terms like “barrier-free”, “wheelchair-accessible”, “universal design”, etc. I described on experience along that line in Wheelchair Friendly Homes Nearing Completion.