No MYSQL is a utility that allows you to set up and maintain an SQL database. As some else said it is free. Most other SQL software like Oracle or Microsoft is aimed at the corporate market and is price accordingly. If this is for personal use or a small database MYSQL should be fine.
SQL stands for structured query language. It the language that you use to input, modify, delete, and manipulate the data in your database.
For the most part SQL is standard across the variations. Most vendors do like to add their own little additional features just to piss off us SQL developers

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