A project file .vcproj / .vcxproj contains settings on how to compile your code into a DLL or a binary file, or something else that the linker can assemble into one unit. A project file is just an xml file that contains compiler settings, linker settings, and describes which files you want to compile.
A solution file *.slnis a text file that groups together multiple project files.
So if you think of it like a tree, then you have got a good mental picture of it like this:
.sln
.vcproj
.h
.h
.cpp
.cpp
.vcxproj
.h
.h
.cpp
.cpp
.csproj
.cs