It’s a common question.
Many believe, that it was the 145.022, powered by the cal. 861. As a result, they refer to the cal. 861 and cal. 1861 Speedmasters as Moonwatches. Technically, the 145.022 was indeed worn on the Moon, so perhaps it deserves the nickname by extension.
If by “Moonwatch” you mean the Speedmasters worn by Neil Armstrong and Edwin “Buzz” Aldrin, it’s a different answer.
The real Moonwatch, if you mean the watch that was worn by the first man to walk the surface of the Moon, is the ref. ST 105.012, powered by the calibre 321.
The 145.022 was introduced in 1968. That’s one year before the Apollo XI mission and two years after the 105.012 was discontinued. It would make sense if NASA had used the brand new 145.022 a year later. However, this isn’t the case.
According to the information published by James H. Ragan, who served as Program Manager at NASA during the 1960s, the 105.012 used on the Apollo XI mission were bought a few years earlier.
As a matter of fact, Mr. Ragan was the one behind the key design feature of the 105.012. This means, that he had a considerable influence on the Speedmaster line itself.
He was the man in charge of the initial tests of the “candidates” for the standard-issue watch for NASA astronauts. It was on his request that Omega introduced the asymmetric case with the crown and pusher guards.
With the 105.012 as Omega’s response to NASA’s requests, NASA would indeed have used these watches a few years before the Moon landing.
The source of confusion
It’s so often wrongly believed that the 145.022 was the first watch worn on the Moon for a reason.
Omega’s advertising did not openly claim that the calibre 861 was the movement in the first watch on the Moon. It always mentioned the Speedmaster Professional as just that, and the Professional name applies to the 105.012, 145.012, 145.022, and all of their “descendants.” If you read between the lines, the claim in the advertisements wasn’t false, but imprecise.
This imprecision is justified, in a way.
Omega supplied NASA with the 105.012, likely also with the 145.012, and with the 145.022. You can’t reasonably expect Omega to know which ones were used on a particular NASA mission.
The officially issued equipment was listed in one place, namely in the NASA archives. That includes issue numbers and the manufacturer’s reference numbers of the watches.
These documents, thanks to Ragan and his cooperation with Omega, surfaced only several years ago. So, for a few decades, the question was impossible to answer. Even for Omega.