going out vs seeing each other

Some examples from the web:

• Money confuses her when it's going out.
• She only thinks about having fun, going out.
• I thought you were going out with me tonight.
• You made me feel really guilty about going out with that girl.
• My European side is going out with you.
• You should be dressed up, going out with boys.
• I like going out with older women.
• Lock the door before going out.
• Victor said he felt like going out.
• Eugene, I'm not going out tonight or any other night.
• Then I started going out with Leonard.
• I miss going out with you on Saturday nights.
• Learn basic techniques needed for going out paddling safely and efficiently.
• They're going out in a shipment of medical supplies.
• NSA just red-flagged a live feed going out on the Internet.
• Sir, the flash about Novakovich is going out.
• It's a dangerous business Frodo, going out your door.
• You going out there by yourself will not look good.
• I thought she was going out with Georgie Wise.
• We might be going out to the country in the morning.

Some examples from the web:

• That's why we stopped seeing each other.
• I think that we need to stop seeing each other.
• Donald and I were seeing each other.
• This is my boyfriend, we're seeing each other.
• When Joe and I started seeing each other we wanted the same thing.
• We... Just started seeing each other.
• And now we have to stop seeing each other.
• ...of any consequence since we stopped seeing each other.
• I felt bad that we stopped seeing each other so abruptly.
• But we started seeing each other, anyway.
• You're not happy Genevieve and I are seeing each other.
• We started seeing each other now.
• I think we should stop seeing each other.
• She and Marcus have been seeing each other.
• Dominic and I are seeing each other.
• We talked and started seeing each other.
• We talked and started seeing each other.
• Yes, but mira, we have to stop seeing each other for a while.
• Fitz forced us to stop seeing each other.
• So I wanted to tell you that we are seeing each other.