The key to understanding the implied meaning of this word (for there do be a large discrepancy between the definitions) lies in knowing the sex of the person uttering it.
Male: For the most part, a man will only use the word cute to describe a woman who's attractive, but not hot, nor dressed to make herself look like a sex object. The kind of girl your mother would want you to settle down with.
Female: When a woman says that something is cute, what she means is that it's something she perceives herself as able to control. It gives off the appearance of being weak, defenseless, small, needy, and undeveloped; something she thinks she could possibly mother, although it will probably grow into a strong, self-sufficient being later on. Nearly any mammalian baby that isn't hideously disgusting in apperance (humans aside) is a good candidate for the female version of the "cute" label. Every once in a while you might hear them refer to certain parts of a man's anatomy as cute (the phrase "cute butt" comes to mind), but I'm pretty sure they're just desperately trying to act like they can be as superficial as men are in the mate-selecting game (this is not possible).
This concept was inspired by the stupid women in the movie Evolution who thought that the little green creature hiding in the kitchen closet was cute because of its timid, helpless, puppy dog face, in spite of the fact that the rest of its entire body was wrinkly and disgusting.