You have to actively choose to install MSYS to get the make.exe. So you should always have at least (the native) mingw32-make.exe if MinGW was installed properly. And if you installed MSYS you will have make.exe (in the MSYS subfolder probably).
Note that many projects require first creating a makefile (e.g. using a configure script or automake .am file) and it is this step that requires MSYS or cygwin. Makes you wonder why they bothered to distribute the native make at all.
Once you have the makefile, it is unclear if the native executable requires a different path separator than the MSYS make (forward slashes vs backward slashes). Any autogenerated makefile is likely to have unix-style paths, assuming the native make can handle those, the compiled output should be the same.