The key distinction is the way and "transport mechanism" by which the age would be verified.
(both in terms of the data security, and privacy)
When I hand my drivers license to a clerk at the grocery store to buy some beer and they take a quick glance at it, it's highly unlikely that that my data and an image of my driver's license is going to be intercepted and end up in a data dump somewhere.
If someone were to purchase that kind of content at a brick and mortar store, it's highly unlikely that the clerk would be snagging a copy of everyone's information in a way that has the propensity for a massive leak and subsequent "Hey, look up your neighbors on the 'here's who's been watching dirty videos, and what kind they've been watching' published leak"
We live in an era where the propensity is high for both stealing peoples' private details, as well as people getting their hands on "dirt" that they can use to damage someone personally/politically/professionally.
In threads where this has been discussed before, I've noted that while I understand the issue they're trying to solve (which is making sure minors can't access that material...and it's a noble cause), good policy needs to have a reasonable benefit to risk trade off.
Meaning, if a policy in question is going to subject a person to some level of personal risk, then the policy needs to be able to demonstrate that it's actually effective enough to address the thing it's claiming to address. Otherwise you've just subjected people to risk for nothing.
Given that 80% of those types of websites are hosted and operated outside of the US (meaning they're not subject to our laws), that's a practical limitation of this proposed legislation.
In reality, and nobody is going to like this answer, this an issue where the cat's out of the bag and we can't unring the bell.
The internet has become ubiquitous, those types of sites make up a huge portion of the internet, there's already been a plethora of tools developed that specifically circumnavigate the monitoring and restrictions people are seeking to enforce, and most parents have already purchased an internet-capable device that their kids have in their pockets and can access when the parents are not around.
These are questions that should've been asked in the 1990's, not in 2025.
It'd be like asking:
"Hey, we already put a package of cookies in our kid's backpack and sent them out to go play with their friends two hours ago -- and gave them $5 that they could technically use to purchase another package to replace it so it wouldn't look like any where missing if they were sneaky enough...how do we 100% ensure they're not going to eat cookies before they come back for dinner?"
Answer: "Sorry, you don't"