There was a "Fixed Roof Coupe" or FRC available from 1999-2000. It had a fixed roof with a short back window and a trunk. The drive train was the same as all other Corvettes. This was the platform used for the Z06 in 2001.
The C5 Z06 was made from 2001-2004 and used the FRC platform. It had a lot of modifications other than just the engine such as thinner glass, rims, trans, fixed antenna, suspension, blah, blah, blah.
All other C5s were either targa top coupes or convertibles.