A cute girl: Imagine short hair (and short height), upturned nose, natural smile, including smiling eyes, and quick to laugh. Shirley from LaVerne and Shirley was cute. Sally Field was cute. A kitten is cute. Pretty signifies a more calm, serene, even serious kind of attractiveness.
These have a similar meaning: the thing being described is pleasing and charming in appearance. In the US, "cute" can refer to male or female persons ("He/She's cute."), or animals ("What a cute dog!"), or inanimate things ("That's a cute outfit you've got on."). "Pretty" is used only for female persons ("She's pretty."); it's derogatory when applied to a male ("Here comes pretty boy.").