What is the Difference between institute and institution?

1) Institute (ORGANIZATION)

it means an organization whose purpose is to advance the study of a particular subject

example:

The National Institutes of Health fund medical research in many areas.

2) institution (ORGANIZATION)

it means an organization that exists to serve a public purpose such as education or support for people who need help.

Example:

a charitable/educational/scientific institution

From what I've read, the two are often interchangable. Institute is often used as part of the name of a specific institution.