Not sure why you said correct, as it's both. A big part of private relay -- I would say the most significant part -- is to allow people to talk to websites without giving up their personal IP (and from that pretty tight geolocation, and with fingerprinting a correlation with loads of other data they collect). Apple makes a big deal about it being about maintaining privacy, not just against snooping of traffic -- which is unlikely -- but against fingerprinting and targeting from the services and sites you connect to.

And to answer the original guy, no Apple does not add any headers or details to tell the destination what your IP address is. They just see that they're talking to an exit node somewhere approximal of your general region.