Homologation basically is type approval. A homologated car is one that is approved to race for a particular sanctioning body. So any race car that is allowed to race in the SCCA is homologated by the club, either implicitly or explicitly.
So why do some cars have homologation papers while others don't? Purpose built race cars which lack a basis in a production vehicle are the ones that need to have paperwork (this since January 1, 1983 in the SCCA.) For Spec cars like the FSCCA and the SRF, the vehicle logbook doubles as its homologation paperwork; for other cars, there is a certificate which normally gets stapled in the back of the vehicle logbook.
Homologation paperwork generally trumps GCR requirements; formula cars frequently have approved construction which doesn't precisely match the GCR roll cage rules. As long as a car matches the paperwork which is on file in Topeka, it's good to go. However, substantial changes which cause deviation from the car as homologated would require revisiting the certification process.
Now, you might ask, how would a tech inspector know that a car has been changed in a way that would trigger a revisit to this process? Well, we don't.
Moreover, there isn't really any transparency to homologation. We in the field really have no insight into what is done when a design is homologated. Does a PE who understands materials and design go through and do the math? I have no idea.