As others have noted, marching is a specific KIND of walking. Unlike some other languages, in English "march" is usually used literally, or close to literally.
"March" always gives us a mental image of soldiers marching on parade.
We have this image even if we just mean one person striding purposefully--"I'm going to march right into his office and demand a raise."
We don't usually "march" just to mean "progress" or "move forward." There is always some idea of rapid, rhythmic, synchronized steps.