They feel similar to butterflies, but where butterflies are that soft fluttering feeling you get when you are excited or happy, The Moths are that sick stomach-flipping feeling you get when you are worried or are upset about something.
The happy fluttering and sick flopping feeling are actually very similar feeling reactions, just one is for a good reason and the other is for a bad. Therefore since moths are the ugly version of butterflies, they represent the ugly verson of the stomach flip-flopping.
When you see your significant other or the person you are interested in enter into the room, you get excited and feel butterflies in your stomach.
When you see your ex with someone else, you get sick and upset and feel The Moths in your stomach.