There are three "official" Oracle tools for managing MySQL in the sense you describe, two of which are currently supported.
MySQL Workbench I assume is the administration tool that's most analogous to SSMS.
mysql command line client is a console utility that allows you to issue queries and get results displayed in "ascii line drawing" tables.
MySQL Query Browser is no longer officially supported, but still available for download and still compatible with newer versions of MySQL Server. It's minimalistic in functionality compared to Workbench, but it's also substantially more lightweight. It's essentially a GUI that's well-suited to a power user who doesn't want "help," just an interface that's more usable for running queries than the command line. (As a DBA all day every day, I use Query Browser and the command line client almost exclusively.)
They're all free, of course.
There's nothing proprietary about MySQL Community Edition, so there's really nothing you can to do, administratively, to a MySQL server that specifically requires one of the official clients. There are others out there, third party graphical tools that can provide, for all practical purposes, any functionality that "official" clients can provide. They all have their respective strengths and weaknesses.
One thing to keep in mind, however, is that if you encounter any unusual behavior in any client, is that you should verify that behavior using the
mysql command line client, to confirm whether it's the client you're using or the server behaving unexpectedly but consistently among different clients.