What is the difference between installing MySQL from generic binaries and from source (compiling it in the kernel)? Are there any differences in a productive environment?
The primary advantage of installing generic binaries is that it saves you time and makes upgrades less complex.
A secondary advantage is that you have some assurance that the binary was built and tested by the vendor themselves, so if you have any doubt about your ability to choose the best compile options for a given platform, and you trust the vendor to do that more, then you can just rely on their choices.
Do verify the binary using checksums. You don't want to have to tell your boss that you inadvertently installed a hacked version of MySQL because you didn't check that the download was the legitimate vendor's binary.
Building from source, you can have a different assurance, that you can document the entire toolchain of compilers, libraries, etc.
You can choose non-default options of the build process. For example, if you want to build against a specific memory allocator library. Or if you want to change some the default values of certain configuration options. Or disable some features that can only be disabled at compile time.
You can apply source code patches for bugfixes, or to add custom features.