Hey here's my new favorite etymology fact: The words scale, scale, and scale all have completely different etymologies

scale as in to climb something comes from latin scala

scale as in the things on fish comes from old french escale

scale as in a measurement device comes from old norse skal

complete false cognates

escale might come from latin as well

since you know, french is a romance language

wiktionary traces it back to skalo in proto-germanic

skal also goes back to proto-germanic skelo

I don't know if those are related

language is wild

Proto-germanic would be closer related to old norse

but skelo and skal are pretty different

is scale like the size of a model relative to the real thing the same word as one of these scales or is it a fourth distinct scale?

it appears to be version 1

To go into more detail on that, the Latin word it comes from refers to a flight of steps or a ladder (itself derived from the Latin word for climbing), with the ladder aspect probably being why it refers to scale as in comparing heights and also the musical scale