From The Art and Popular Culture Encyclopedia
Philosophers sometimes distinguish classes from types and kinds. We can talk about the class of human beings, just as we can talk about the type (or natural kind), human being, or humanity. How, then, might classes differ from types? One might well think they are not actually different categories of being, but typically, while both are treated as abstract objects, classes are not usually treated as universals, whereas types usually are. Whether natural kinds ought to be considered universals is vexed; see natural kind.
There is, in any case, a difference in how we talk about types and kinds versus how we talk about classes. We say that Socrates is a token of a type, or an instance of the natural kind, human being. But notice that we say instead that Socrates is a member of the class of human beings. We would not say that Socrates is a "member" of the type or kind, human beings. Nor would we say he is a type (or kind) of a class. He is a token (instance) of the type (kind). So the linguistic difference is: types (or kinds) have tokens (or instances); classes, on the other hand, have members.
Similarity between the concept of a class, and that of a set defined by its members. Here the class is extensional. If, however, a set is defined intensionally, then it is a set of things that meet some requirement to be a member. Thus such a set can be seen as creating a type. Note that it also creates a class from the extension of the intensional set. A type always has a similar class, but a class does not always have a corresponding type.