"At efterabe" is like the English saying "monkey say, monkey do" - a monkey copying something others do, usually straight after the other person has done. "At efterabe" is also considered rude.
"At efterligne" however is more like mimicking someone. Like when a child sees their mother doing something, they'll try to mimick it, so that they'll learn the skill. Not considered rude unless done several times by an adult - and by then they're "efterabe"-ing.