Is there a difference between arousal and an erection?
An erection means your penis increases in size and gets hard. It typically does this whenever your interest in sex arises, but it can happen when you are not thinking about sex. For example, men have erections while they sleep and you typically see the last erection when you wake up in the morning. When you first gain the ability to have erections, you frequently get spontaneous erections for no apparent reason. This usually settles down when you get older.
Arousal means your interest in sex has been triggered. While it can be accompanied by an erection, it doesn't necessarily happen. It could be as mild as an increase in heart rate causing your skin to flush, or noticed because pre-ejaculate fluid drips from your penis.