DB-Library was the original client lib for Sybase. It was written in the mid-80s. CT-Lib (Open Client) was supposed to be its replacement -- one that made the api more consistent; however, CT-Lib was significantly different enough that a lot of installations never migrated to CT-Lib so DB-Lib has been kept around.
The general consensus is new work should use CT-Lib but I would recommend using which ever you're comfortable with (after being deprecated for 20 years now, I doubt the trigger will ever be pulled on DB-Lib). That being said, if you're looking to use perl and Sybase, I would recommend DBI and DBD::Sybase (which is built on top of CT-Lib) rather than any of the Sybase modules. mpeppler maintains them so if he pipes in, ignore me and listen to him.