@epi non-countable is better than uncountable. non is that is not counted. un is that is impossible to count. There is no confusion. When we say a type of chair or types of chair in English, we mean a category of chair. Chair becomes a style or category of chair; not actual chairs. So, there is no confusion at all.
Discussion on answer by Lambie: 'One …
Discussion on answer by Lambie: 'One …