Sounds to me like these approaches to "time of first sex" are really just a matter of degrees and definition of "relationship", rather than polar opposites as they first seem.
Some people have a rule of "no sex before marriage". I personally knew a couple where the girl said "no sex before engagement". Some say "no sex on the first date". When you think about it, these are all just different degrees of "no sex before a certain level of commitment" where
marriage > engagement (formally committed) > informally committed > dating > went on one date
Then the question comes down to which stage you define as "in a relationship". yellowtamarin's and Cafeaulait's approaches are not necessarily different, depending on that definition. Some people may consider it a "relationship" if they've gone out on 3 dates and are not dating anyone else, but haven't had sex yet. Sure, the relationship may end immediately after the first time they have sex, but that's a different story.

To me, a relationship means both individuals have decided that they are in a relationship and they are 'exclusive'. I also cannot have sex with someone if I am not in love with the person. Off course, there has to have been some sort of physical interaction before I change my facebook status to 'in a relationship'.