The two words both refer to a group of something and the main difference between the two can be the context in which they are used. Kind is used in general, everyday conversation and type are followed by the preposition 'of' as in a sentence. Variety is also used as an adjective to describe someone, as in, she is a kind person.
Type is used in the sense of subdivision or category; however, the word kind is used in the spirit of a sort, and it does not have such informal use attached to it. Both type and kind have to concur with the noun with which they are used.
Often, there are words that are so close in the definition that they are used interchangeably. Two of these words are kind and type. However, there is a difference between kind and type. The main difference has to do with their definitions. Type means that the traits that a thing has and makes it a certain type is distinct.
There is no ambiguity with the types and those things that are considered to be those types. Kind has some ambiguity. Therefore, if you are wanting to be specific and assured by describing something, your best answer would be type instead of kind. So, you may want to start using the word type instead of kind from now on in order to be more specific.