When I was a child, when someone tried to butt in front of you in line, kids would say, "No butts, no cuts, no coconuts!" Hehe :-)

Cut in line is more common. "Butt in" is usually used to mean "interrupt". E.g. "It's rude to BUTT IN when someone is trying to explain something!"

They are the same. You could say He cut in line. Or you could say he butted ahead of me.