There are many ways to define dating, based on these definitions, you will understand better how dating works in American culture.
- Seeing someone/casual dating = casually dating, you may be also dating others, or not, and the frequency is low (say once every couple of weeks or so, or even once a week but you don't talk much in between). Movie dates or informal group dating.
- Dating/casual dating means the two of you are almost dating exclusively but have not really talked about it. You see one another anywhere from 1 to 3 times a week. You have not discussed exclusivity.
Exclusive or serious dating means you have discussed being exclusive, meaning, you will not date others. But you're not talking about anything beyond being exclusive. In the old days they called it going steady.
Exclusive might lead to something more serious, or not. In my opinion exclusive is merely what it says, you don't date others, but it doesn't necessarily mean that you will have a bigger or permanent commitment. It's still part of the getting to know you, only on a more serious and committed level.
If you are exclusive with someone, then it is not acceptable to see someone else and this would be considered cheating. "Going out" would suggest exclusivety. If you are dating more than one person, you should make it clear to them that your relationship is not exclusive.