Databricks SQL is the Product Name. 
https://www.databricks.com/product/databricks-sql

Spark SQL is the SQL interface (SQL commands) that run by utilizing the power of Spark as a computing engine.
https://www.databricks.com/glossary/what-is-spark-sql 

MSSQL (assuming you're talking here about MSFT SQL Server) is a relational database management system developed by Microsoft and the language it supports is also SQL but has proprietary functions etc that only work there. Similar to how Oracle would have PL/SQL.

All of these "SQL" variants try to align to the ANSI standard but each engine can have it's own extensions, functions etc, so some of your code might be transferrable from system to system but lots of it won't be.

This is why you need transpilers like https://github.com/tobymao/sqlglot to help with those conversions.