Question about the issue in the two-tier model of marriage and consecration

Hello Rabbi
The rabbi occasionally speaks in articles about the two-tiered model of kiddush and marriage.
That Kiddushin in Judaism refers to marriage, meaning a legal-halachic reference to a general human situation.

I wanted to ask if there is a halachic difference in understanding the two-story model compared to the more common understanding in the yeshiva world (to my understanding)?

That is, between understanding the concept of Kiddushin as an intentional mitzvah that comes on top of natural marriage (the two-story model)
and the understanding of the concept of kiddushin as the forgiveness of marriage in itself (in my understanding, this is the more standard concept in the yeshiva world)
In fact, the second view is a view that does not see the two-story model, but sees two buildings next to each other.
In this image, the Gentiles enter the structure of marriage, and if the Jews did not perform Kiddushin, they did nothing, even if they were in a relationship and even if they wanted to formalize their lives in a “serious” relationship.

thanks