I think you're on the verge of getting it.
My guess is that the 'ownership rate' is an estimate, while the 'registered ownership rate' is exactly what it indicates.
Now, stop and think about the California numbers. If California has an 'ownership rate' estimated at 16.3%, that means they are estimating 6,357,000 gun owners in California.
If they are claiming a registration rate of 10.34 per 1,000, that means a registration rate of 0.01%.
While that may 'feel' wrong, bear in mind that the 4473's only show purchase, not current possession. The so-called 'assault weapons' registration was nearly a complete bust. In short, while the numbers may be 'exaggerated,' it is representative of where their thinking is in terms of not knowing who has current possession.
Now, just because legal gun owners are not the primary problem, that doesn't change their thinking. It's why they've passed laws with regard to reporting stolen/missing guns, so-called 'assault weapons,' etc. They feel that by knowing who has the guns in their possession, they can 'control' the use of those guns.
We know that's not the case and we know that 'registration' is most likely to be met with 'Irish Democracy;' but, to them, it's about 'control.'