I think there are similarities. In places liked NYC, it can be very competitive but I think that more students participate in EC outside school (sports, music, etc), so you might not see those things creating hooks the way they would in a BS. Sure, it’s great that a kid is a top violinist but she’s probably going to stick with her prestigious youth orchestra over anything the school does. Likewise, there may be more activity around connections (in admissions) at some day schools.
The biggest difference, of course, is that day schools are limited to what is commutable. This means it’s probably easier to understand the pool… Remember too that BS are screening for kids who will be able to function very independently and who will be able to create “family” in their community. That kind of social “fit” matters far less when a kid goes home every night.