SQL is a standard language for relational database management system (RDBMS).
MySQL is an open source RDBMS with its own dialect of the language controlled by Oracle.
PostgreSQL is an open source RDBMS with its own dialect of the language.
Sql Server is Microsoft's RDBMS and using the T-SQL proprietary dialect of SQL.
SQLite has a SQL dialect but it is flat file based. I think its useful for development or a program that needs a local, light weight database; however, it wouldn't be useful for concurrent users.
When you get started, download a sample database. Sql Server has Adventure Works sample database.
When developing you want to use the standard SQL as much as possible. Don't pull out the nifty features out of that particular implementation unless you have to. It makes your code and knowledge more transferable.