This may be a matter of terminology not being standardized all around the country or world. What you describe is exactly what much (most?) of the USA calls “independent living”, not “assisted living”.
In “assisted living” as the term is defined here in FL and other states, a staffer walks into your unlocked kinda-like hospital room, minus the beeping medical gear, every hour to check on you. They feed you your meds on their schedule. They probably spoonfeed you your meals, also on their schedule. And accompany you on whatever little walking with assistive devices you’re able to do. The only time you’re alone is in bed. Which is where you are most of the day.
There’s a vast gulf in quality of life between the two. And clearly somebody who needs the level of life management that my definition of “assisted living” provides, could not possibly survive on their own in the situation your parents have.
Last things first.
They aren’t the sorts of places I wish to live in either. But I don’t get to choose my end-trajectory. I may be dead just after hitting [Send] on this post. Or I may be fine to age e.g. 88 then unable to walk for the remaining 10 years of my time on earth. My goal now is to have a variety of plans at least thought about, so that increasingly lazy senile me isn’t suddenly or slowly confronting a completely new world I know nothing about and haven’t even thought about.
If I’m too infirm to safely cross the street, I’d kind of like having a restaurant in the same building I can dodder to within a couple hundred feet. And all indoors, especially for folks in snow country.
If I turn out to develop Alzheimer’s, or simply outlive most of my brainpower, well, something is going to happen with my still kinda intact body. I want a plan for that possibility too.
Simply wishin’ and a hopin’ it won’t happen to you is not a plan. Well, it is a plan; a plan to fail. Unless you have the extreme good fortune to drop dead while still quite spry. But if that happens, you also missed out on at least several would’ve-been-good years. This game sux; the only way to win is not to play.
That is a large question worthy of a large post I’m not going to write right now. Let me put this down as a marker for that. In many ways, you’re right that there’s not much difference.
As long as you’re mentally together enough to make and use those arrangements. Really old people become not only more stupid, but less ambitious and unable to make even simple decisions, despite understanding the need to do so and the alternatives on offer.
A problem with any arrangements you may make, e.g. bill paying, or home help, or prescription delivery, is that nothing you set up stays set up. Everything needs occasional attention if for no other reason than your vendors are always “improving things for your convenience.” A quality IL facility takes care of many of those things.