Both DB-lib and CT-lib are libraries that implement the TDS protocol from the client side.

DB-lib

DB-lib was Sybase's first version. It was a good first attempt, but has/had a number of inconsistencies. There are, or possibly were, a lot of applications written using DB-lib. If you are about to start a new Open Client development, consider using CT-lib, it is the preferred choice. (What version of TDS does DB-lib, is it only 4.2?)

Having said that you should use CT-lib for new developments, there is one case that this may not be true for and that is 2 phase commit. 2 phase commit is supported directly by DB-lib but is not supported directly by CT-lib.

CT-lib

CT-lib is a completely re-written version of Open Client that was released in the early '90s. The API is totally different from DB-lib, and is much more consistent. Applications written using DB-lib cannot simply be compiled using CT-lib, they need a significant amount of porting effort. CT-lib is newer, more consistent and, in several people's opinions, including mine, slightly longer winded. Having said that, the future of DB-lib is uncertain and is certainly not being developed any more, as a result all new apps should be written using CT-lib.