Some features that aren't really called out from comments I've seen so far.
Static linkage (.a/.lib)
Sharing memory between these compilation units is generally ok because they should(?will) all be using the same runtime.
Static linkage means you avoid 'dll hell' but the cost is recompilation to make use of any change at all. static linkage into Shared libraries (.so) can lead to strange results if you have more than 1 such shared library used by the final executable - global variables may exist multiple times and which one is used and when they are initialised can cause an entirely different hell.
The library will be part of the shipped product but obfuscated and not directly usable.
Shared/Dynamic libraries (.so/.dll)
Sharing memory between these compilation units can be hazardous as they may choose to use different runtime. This can mean you provide different Shared/Dynamic libraries based on the debug/release or single/multi threaded or...
Shared libraries (.so) are less prone to 'dll hell' then Dynamic libraries (.dll) as they include options for quite specific versioning.
Compiling against a .so will capture version information internal to the file (hard to fake) so that you get quite specific .so usage. Compiling against the .lib/.dll only gives a basic file name, any versioning is done managed by the developer (using naming or manually loading the library and checking version details by hand)
The library will have to ship with the final product (somebody else can pick it up and use it)