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What's the difference between the Nashville Number system and a Roman Numeral System?

A question was asked ealier showing the below chart. At first, I thought this was the Nashville number system, but was informed that the Nashville number system uses 1,2,3, etc., not roman numerals.

Is there a formal name for the system that uses Roman numerals? And how is that system different than the Nashville number system.

enter image description here

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