Correct, though the "natural" vs not still applies here. There's no evidence or scientific reason to suggest that catching COVID-19 naturally provides any different immune response than receiving the vaccine for the same strain.
In my previous comment I was unclear about what I was addressing and when, though ultimately the point is that this distinction of contracting a virus "naturally" versus "artificially" is not scientifically based. Applies to COVID-19 mRNA vaccines as well as flu vaccines.
If there's evidence to suggest otherwise though we should get that out there.