What is the difference between "Type Certificate" and "Certificate of Airworthiness" for an aircraft?
A Type Certificate is a certificate that the FAA gives the manufacturer of an aircraft, certifying the design of the aircraft. So for instance, Cessna Aircraft Company of Wichita, KS holds a Type Certificate for the Cessna 172. Notice that the certificate specifies what components make a Cessna 172, what its limitations and performance specifications are, and so on. When Cessna makes a 172, that aircraft has to conform to this specification. Moreover, only aircraft that meet this specification are certified as a 172. Which is why, if you make a major modification to a certified aircraft, it requires an STC-- a "Supplemental Type Certificate," to confirm that with the new equipment, the aircraft design is still airworthy and the limitations are accurate. But there is only one Type Certificate for an unmodified Cessna, and it is issued to Cessna, Inc.

On the other hand, an Airworthiness Certificate is issued for each aircraft individually and certifies that this here particular airplane is airworthy. They can be revoked if the airplane undergoes, for instance, an accidental major airframe modification (or indeed, an uncertified major alteration of any kind or if for some reason the FAA has reason to believe the aircraft is no longer airworthy). Each aircraft has its own Airworthiness Certificate that is displayed in the passenger compartment, and thus there are as many Airworthiness Certificates for Cessna 172's as there are airworthy 172s.