The "er" in closer means "more" that is to say "more close". But the words "close" and "closer" can both have physical and emotional meanings. Context is required to distinguish between the two cases. "They are getting closer to each other." - This could mean literally they are now physically closer (less distance between them) but also it can mean that they are emotionally closer or as you say "they are getting along with each other" more than previously.