Linker scripts change whether or not symbols are added to a global symbol table for subsequent requests (i.e. "exported"). Though, you don't even need a linker script to effect visibility as both GCC and clang provide a visibility function attribute, and you can change the default visibility through a simple compiler command switch.

dlopen permits you to control whether exported (externally visible) functions in a module become available to satisfy link dependencies in the application, such as subsequent module loads. See the dlopen flags RTLD_GLOBAL and RTLD_LOCAL.

dlmopen is for controlling the visibility of shared library dependencies pulled in by dlopen'd modules, whether RTLD_GLOBAL or RTLD_LOCAL, which only effect the immediate symbols in the module and not symbols from automatically loaded shared library dependencies. If you link the main application with OpenSSL (-lssl -lcrypto), or a prior module you dlopen'd pulled in OpenSSL as a dependency, then those OpenSSL symbols become available to satisfy requirements for subsequent dlopen'd modules. dlmopen allows you to create an entirely different symbol namespace for a module or modules, where symbols dependencies are only ever satisfied from that namespace, and exported (global) symbols, whether pulled in by dlopen or transitively via a shared library, are never visible outside that namespace.

None of these options directly map to the behavior of DLLs. DLLs fundamentally use different semantics, AFAIU. The closest behavior to DLLs might be DT_RUNPATH + dlmopen, but dlmopen use is explicit so not really the same thing. You could use ELF symbol versioning (maybe in combination with DT_SONAME and DT_RUNPATH) to accomplish the same thing as DLLs by effectively renaming all the symbols in a library (e.g. attaching a version component), but there aren't any tools around to help automate that, AFAIK; you'd have to generate linker scripts and it'd be a complex build. Much easier to just static link at that point.