1, The full form of SSDT is SQL Server Data Tools

SQL Server Data Tools (SSDT) is a modern development tool for building SQL Server relational databases, Azure SQL Databases, Analysis Services (AS) data models, Integration Services (IS) packages, and Reporting Services (RS) reports. With SSDT, you can design and deploy any SQL Server content type with the same ease as you would develop an application in Visual Studio.

2, The full form of SSDT if System Service Dispatch Table

System Service Dispatch Table or SSDT, simply is an array of addresses to kernel routines for 32 bit operating systems or an array of relative offsets to the same routines for 64 bit operating systems.

SSDTs used to be hooked by AVs as well as rootkits that wanted to hide files, registry keys, network connections, etc. Microsoft introduced PatchGuard for x64 systems to fight SSDT modifications by BSOD’ing the system.

When a program in user space calls a function, say CreateFile, eventually code execution is transfered to ntdll!NtCreateFile and via a syscall to the kernel routine nt!NtCreateFile.
Syscall is merely an index in the System Service Dispatch Table (SSDT) which contains an array of pointers for 32 bit OS’es (or relative offsets to the Service Dispatch Table for 64 bit OSes) to all critical system APIs like ZwCreateFile, ZwOpenFile and so on..