SSDT is a universal, declarative model that expands all the phases of database development in the Visual Studio IDE. BIDS was the former environment developed by Microsoft to do data analysis and provide business intelligence solutions. Developers use SSDT transact- a design capability of SQL, to build, maintain, debug and refactor databases.
A user can work directly with a database or can work directly with a connected database, thus, providing on or off-premise facility.
Users can use visual studio tools for development of databases like IntelliSense, code navigation tools, and programming support via C#, visual basic etc. SSDT provides Table Designer to create new tables as well as edit tables in direct databases as well as connected databases.
Deriving its base from BIDS, which was not compatible with Visual Studio2010, the SSDT BI came into existence and it replaced BIDS.