The difference is covid is comparably very survivable (but grants less enduring immunity), the burning out is a product of immunity combined with death. Herd immunity was dismissed as a strategy because as a policy killing a massive number of people very quickly was not viable, but it is nonetheless going to eventually be the outcome in some form. However the fact that immunity from vaccines and infection fades seemingly pretty quickly means that point will be further out, and once reached will not mean the end of the disease but it will not look like it did in this, the period of fast burn. Hard to know where it will land then but I'm just throwing out a guess of maybe 2 million - 4 million people a year dead.

This is well-trodden territory, but the Spanish flu is the best point of reference here, it burned through the world killing hundreds of millions of people, went through multiple stages, stuck around for a few years, burned out, and then remained skulking around killing a great deal of people but was done as a pandemic.

You don't need Black Death level deaths for that to happen. The Spanish Flu pandemic burned out rather quickly.

I expect the end of covid will probably take more death the Spanish Flu, but probably closer to that than anything else. (We don't really know why the Spanish Flu ended so suddenly, but I'd expect being a flu played some role.)