What's the difference between "kind" and "type"?

In short, type is used to differentiate one group from the rest and kind is used to link an individual to a group. They are sometimes interchangeable, but not always.

Type refers to clearly distinguishing and essential characteristics or traits shared by members of a group. Its root meaning is "impression."

O+ is the most common blood type in the United States of America.

To mankind in general Macbeth and Lady Macbeth stand out as the supreme type of all that a host and hostess should not be — Max Beerbohm.

Kind, on the other hand, usually refers to a group trait that is shared innately by the members (see "mankind" above). Its root meaning is "race" or "offspring."

The true test of civilization is, not the census, nor the size of the cities, nor the crops, but the kind of man that the country turns out — Ralph Waldo Emerson.

The rule which forbids ending a sentence with a preposition is the kind of nonsense up with which I will not put" — misattributed to Winston Churchill.

Interchangeable use:

She's not that kind/type of person. She is not nasty. She's very nice.

See examples below:

She's not my type. (=I'm attracted to a different kind of girl)

She's not your kind. (=She's a fundamentally different sort of person)

See link1 and link2.

I'm afraid it's rather nebulous and very context dependent. Both can be very general or very specific depending on what you're talking about. For this kind (or type) of general purpose use you can regard them as equivalent.

I'm not a native speaker, but to me it looks like this:

• type — if the thing can be further subdivided, into subtypes or kinds;
• kind — if there is no further subdivision.

Came to this conclusion after reading this page on Yahoo Answers.

I always understood type to refer to typology where there is an antitype–type representation. Kind is a grouping by classification.