No, there is definitely a difference between age verification and adult verified to LL. Otherwise there wouldn't be a need for LL to explain the difference. PIOF used to be the way that LL verified you as an adult but they went to the age verification process due to a vocal minority's prompting and the desire to attract more real world businesses, schools and the like. Places which identify as mature may also be required to want the age verification even if on mainland if I recall correctly.
This is not a stab at you or your friend, but an attempt to keep misinformation from causing an outcry. I personally do not believe that if a minor can manage to get ahold of their parent's or another adult's credit card or paypal information that they would have any trouble getting ahold of their driver's license, social security number or passport information as well. The difference, I believe, is that the age verification is more of a formal and legally satisfying manner to assure that only adults access adult content, while the PIOF of the past was more a company policy which was only intended to assure LL itself. Age verification gives LL the ability to point to a process which can reassure those types of residents that they are wishing to attract and the vocal minority of residents already in world who want it.
Edited to add: Honestly, though, I can't see how you can consider giving the information to get your profile flagged as PIOF to NOT be giving personal real life information to LL. In fact, you give that information directly to them, not to some annonymous company which claims that it discards the information or at least does not share it and it is just where it could hurt you to do so, in the bank account, if it fell into malicious hands. It took me longer to do the PIOF than it did to get age verified, personally.