Those are called nose augers. They usually required a pilot hole or divot to get started. They are used to bore a very straight hole across the grain. Bits with curved cutting lips will not follow the grain, like Cooks, Gedges, nose, spoon, etc. That set most likely belonged to a shipwright with the long shanks and interchangeable handle. It was probably used to bore holes for bolts or pins.
I have also seen them called blind augers and lip augers, I think, but am not sure.