Very often it makes no difference which of these words we use. But good dictionaries point out some subtle differences. In fact, sometimes only one of these words is correct. For example, it would be wrong to use ‘sort’ or ‘kind’ in sentence 1 below. Compare these three English sentences: 1. What is your blood type? (Expected answer is a precise named category.) 2. What sort of prices do they charge? (Expected answer is a description rather than a named category.) 3. What kind of dog is that? (Probable answer is a named category, but not necessarily as precise as 1 above. A descriptive answer is also possible.) So … ‘type‘ usually means a precisely defined category. ‘sort‘ is more general, often about character rather than definition and can be used in a negative way e.g. What sort of person would do a terrible thing like that? ‘kind‘ is about half way between, usually referring to large categories or families of things that are naturally related. Note that ‘type’ cannot be used as a hedge phrase, as in ‘She’s a bit sort of (or kind of) upset about it.’

They can all mean the same thing, but all of these words have multiple meanings so it is highly dependent on context. :)

Sort and kind are informal but type is formal