You’re right, and think it’s settled
Omega has lent to Swatch only it’s case and dial design, and branding (“Omega,” “Speedmaster,” and “Moon(S)watch”) for a set of watches that are otherwise composed of Swatch’s bioceramic and its 4 jewel quartz chronograph movement, with the little planets on back being the battery covers. Here’s one of Swatch’s current ($175) quartz Chronos:
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