difference between math and math.h

What is the difference between math and math.h. I check some compilers use and .h extension and others don't. How do we know when to use what?
math.h is a C header.

math is something I've never heard of in this context.

cmath is a C++ header that contains the same functions as math.h, and some extra ones, but written in C++ where appropriate and all inside the std namespace.

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