The stand-alone runtime libraries that are needed depend on which version of Visual C++ you are using to build.
It looks like you can find the one you will need (for any system that runs your builds) here:
https://learn.microsoft.com/en-us/cpp/windows/latest-supported-vc-redist?view=msvc-170Remember that this library needs installing on a system before they can run your builds. This isn't a massive deal (I've seen many apps/games requiring these before installation) but you may want to have a way for end users to install it first (it shouldn't install if it's already on the system but if it does, it'll just replace/update it).
If you're using static (rather than dynamic) SFML libraries, you're including the libraries into your executable file so there would be no DLL (dynamically linked library). An exception is that the audio dll (openal32.dll) due to its licence.
Is "the same behaviour" the 'correct' behaviour? Does this mean that running the executable directly causes it run correctly? Have you tried it in a separate folder (with just the files you are wanting to distribute - not the installation version)?
Another thing to consider is if you're (accidentally) using an absolute path for some file, it'll likely fail to find it on other systems.