No, they are not the same thing. The fact that a transfer of money happens is not a sufficient criterion for defining insurance.
Take two people with different risk profiles but who are both insured. If you can tell a priori which one is expected to have lifetime claims that exceed their lifetime premiums, then you don't have insurance - you have a wealth redistribution scheme[0].
Note that I didn't specify which person had the greater risk profile, or whether they both purchased the same "tier" of plan, or even whether they purchased their insurance from the same insurer. This property of insurance still holds even if the two people have completely different risk profiles, if one purchases a gold plan and the other a bronze, and if one person purchases from MegaInsurance in New York and the other purchases from AcmeInsurance in California - as long as they are both insured at risk-adjusted rates.
> You do realize that this is functionally the same as getting rid of the preexisting conditions protection, right? Whether someone pays tens of thousands to a doctor for care or to an insurance company for coverage are in practice exactly the same. The whole point is that many of us think that is a fundamentally unfair system to force someone to face in that situation.
First, nobody is paying tens of thousands of dollars to a doctor, because there's an out-of-pocket maximum cap. (And that cap could still exist under a risk-based pricing world.)
Second, it's not, functionally the same, because that doesn't mean that you can't separately provide income- or wealth-based subsidies if you're aiming to redistribute wealth. But that happens at a completely different layer from the risk underwriting - and because the underwriting process is allowed to properly account for a person's risk profile, you end up with lower aggregate premiums (pre-subsidy). Lower unsubsidized premiums means that you don't need to subsidize as much money in order to achieve the same sticker-price premiums that consumers see - in other words, the entire process is significantly cheaper for what appears to be the same result to the patient.
The reason we don't do this, even though it would be significantly cheaper, is because it's politically infeasible.
[0] Which, you may note, is currently the case - and that's because health insurance as it stands is a mishmash of two completely unrelated products ("insurance" and "wealth redistribution") that we happen to try to stuff into the same box.
