Correct. The synthetics are clear. In my view, the strategies often aren't similar. Most people selling naked puts are doing so OTM to "bottom feed" for stocks on the cheap, with the knowledge that the small profit they get when not assigned is at least money in their pocket. Most people selling covered calls are doing so OTM so as to "juice" their returns, with the knowledge they are limiting their upside on a big run. The two are not synthetic because the strikes are not equivalent.
You missed the point.
If A = B then you can do either one of them and get the same result.
If A does not = B then they do not provide the same result.
We are talking about when A = B.
You are talking about when A does not = B and that isn't a synthetic.
IOW, when it's the same series, the two strategies are equivalent. When different, they are not.
As many here regularly point out, why do the simultaneous B/W and incur more frictional costs (B/A and commission) if you can do same series short put?