Rapport is the feeling of "being at the same wavelength", as if you understand each other and connect deeper than normal. It has nothing to do with sexuality. It is just a social thing. You can build rapport by synchronizing your body language, tonality and how fast you talk with the girl. Use the same kind of words and expressions like her, and she will feel that you understand her better. It takes time to build rapport, so it can never come first.

Attraction is something sexual. In the context of pickup, attraction always come first. The girl needs to think you are an attractive guy long before you even speak to her. However, in contrast to other theories, I think attraction is something you need to maintain throughout the entire interaction with the girl.

The word "connection" is probably just confusing here. I would rather use "comfort" or "relationship". "Connection" can be a combination of "rapport" and "relationship".

Pickup goes like this:

Attraction -> Build rapport, create comfort and a relationship (get to know each other) -> Seduction