For a static library, the code is extracted from the library by the linker and used to build the the final executable at the point you compile/build your application. The final executable has no dependencies on the library at run time
For a shared library, the compiler/linker checks that the names you link with exist in the library when the application is built, but doesn't move their code into the application. At run time, the shared library must be available.
The C programming language itself has no concept of either static or shared libraries - they are completely an implementation feature.
Personally, I much prefer to use static libraries, as it makes software distribution simpler. However, this is an opinion over which much (figurative) blood has been shed in the past.