Clang is a C language family frontend for LLVM. That is, it's a compiler for C and C++ and related languages.

Libc is the C standard library, and there are multiple implementations of it, e.g. glibc and musl. Clang does not include an implementation of libc, though it does have an implementation of the C++ standard library called libc++: https://libcxx.llvm.org/

It's not immediately clear to me why an LLVM implementation of the C++ standard library would be desirable while an implementation of the C standard library would be undesirable.