What you're really describing is the difference between approaching women for sex and approaching for relationships. The reason the former seems different and "new" is because casual sex has become more accepted over time. When women didn't put out as easily, going purely to "pull" was less effective.
I don't really recommend making slow, casual advances though. I don't see that as more traditional either, if anything I see this as a modern thing - that you're supposed to pretend you aren't actually dating, that you're just "hanging out". Although it does work in some cases, it can be a waste of time and it can also cause a woman to not see you sexually. Confident men will establish their interest early on. That's not a bad thing - everybody wants to be sexually attractive and a man who makes that clear appears in control and therefore attractive. He's also more honest. From the moment you meet a girl you like, you see her as sexually attractive and you know you want to sleep with her eventually. Women know that, and they also want men whom are true to themselves. What you're looking for is a middle ground between the guy who pushes for sex and the guy who pretends he's asexual.
I would say the men I've dated have had a "traditional" approach to dating. What that means is that we meet in whatever manner, they ask for my phone number, then call or text to ask me out to dinner. We have dinner, just the two of us in a nice restaurant, share a hug/kiss, then he asks me out again, so we're dating and at some point we'll sleep together.
And actually passed?