The two aspects: by myself......alone by myself, myself.....on my own initiative. I built it myself, but not by myself.........It was my idea and I supervised the construction, but some friends helped me. I drove the car myself, but I wasn't by myself: there were passengers in the back seat. Did you take the bus to school? No, I went to school by myself with some friends. My Dad said that I am allowed to take the boat out on the lake by myself as long as I'm with friends who know how to swim.

They both have no differance and share the same meaing, but there is a couple meanings to both sentances, one being that literaly set (that) person went to school alone, and secondly that set person went to school without any help.