I don't know that the resume needs to be formatted differently. But startups and FAANG companies may be looking for different sorts of people.

In my startups, what I'm looking for is primarily three things: that the applicant's interests are in line with what the startup is doing, that the applicant will mesh well with the rest of the team, and that the applicant is good at problem-solving and working without a great deal of supervision.

The specific skills the applicant has are important, but probably not "top 3" important. As long as I'm comfortable that they enjoy learning new things and are good at it, any specific skill they lack can be provided through training.

A resume/CV that makes it easy for me to see how the applicant matches those needs is one that is more likely to successfully get a callback from me.