How does gcc search framework headers on Mac OSX(10.15)?

Question

By gcc -v I know that gcc searches in these paths:

/usr/local/include
 /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/lib/clang/11.0.3/include
 /usr/include
 /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include
 /System/Library/Frameworks (framework directory)
 /Library/Frameworks (framework directory)

I write:

#include <CoreFoundation/CoreFoundation.h>
int main() {
        return 0;
}

It gives no error messages. But with the following, gcc cannot find the header.

#include <CoreFoundation.framework/Headers/CoreFoundation.h>
int main() {
        return 0;
}

I know that gcc finds the header CoreFoundation.h in /System/Library/Frameworks. And the path of the header is /System/Library/Frameworks/CoreFoundation.framework/Headers/CoreFoundation.h.

My question is: why #include <CoreFoundation/CoreFoundation.h> is OK? Why not CoreFoundation.framework/Headers/CoreFoundation.h (it gives error messages)? I think it should be CoreFoundation.framework/Headers/CoreFoundation.h, as the full path of the header is /System/Library/Frameworks/CoreFoundation.framework/Headers/CoreFoundation.h, and the inlcude path is /System/Library/Frameworks.

Thanks in advance.

The following may have something to do with this problem.

I compile a file that include 'CoreServices/CoreServices.h'.

did not find header 'CoreServices.h' in framework 'CoreServices' (loaded from '/System/Library/Frameworks')

Then I use gcc -I /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/CoreServices.framework/, because I know the header's path is /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/CoreServices.framework/Headers/CoreServices.h. But it still doesn't work. Why?