It has uses in both C and C++.
As you guessed, the static part limits its scope to that compilation unit. It also provides for static initialization. const just tells the compiler to not let anybody modify it. This variable is either put in the data or bss segment depending on the architecture, and might be in memory marked read-only.
All that is how C treats these variables (or how C++ treats namespace variables). In C++, a member marked static is shared by all instances of a given class. Whether it’s private or not doesn’t affect the fact that one variable is shared by multiple instances. Having const on there will warn you if any code would try to modify that.
If it was strictly private, then each instance of the class would get its own version (optimizer notwithstanding).
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