"What's the diff. between dating and seeing someone? Is dating a step up or the opposite?"
The general definition of "dating" can either mean "going on dates" or "in a relationship" (aka "going out"). "Going on dates" is casual, not-so-serious, and not necessarily exclusive. It's usually the trial (and error) stage when you first start to consider getting into a relationship.
When you're "in a relationship" or "going out with [someone]", it's usually exclusive, and lends a title of "significant other" to the status. This is the stage when you would feel obligated to call the other person to let him/her know what you're up to, especially if you're free that night.
"Seeing someone" is somewhere in the middle -- when you're going on dates, perhaps even "hooking up" on a regular basis, but not officially in a relationship. There's romance and there's probably intimacy, but if you were to stop seeing each other, it doesn't actually qualify as a break-up -- because you weren't officially together in the first place. It's the same level of intimacy/official-ness as "friends with benefits." That said, "seeing each other" has a more progressive connotation, because you're still getting to know each other and could still evolve into dating, whereas "friends with benefits" can have a more stagnant/established/"scratching a mutual itch" feeling.
The usual evolutionary scale is:
- Going on dates (dating / "We're going to dinner...")
- Seeing each other (hooking up / "We're kind of together, but i don't need to change my Facebook status yet...")
- In a relationship (significant other / "This is my girlfriend/boyfriend. We're going out. Woohoo!")
In the end, though, the best way to determine what "stage" you're at with someone is to just be straightforward and talk it over. "Do you want to be exclusive?" (Just make sure that you know what your answer would be, too, if you were asked the same question.) It's usually safer to start on dates with one person at a time, so that you don't hurt any feelings. Be nice! :)
Interestingly, a bit of a Google Search turns up the following links that also tackle this question: