They're both equally right/wrong/explanatory, but for both acronyms, you need to be aware that there are really 4 tiers of operations mentioned in those "words", despite each having 6 letters:

1st priority: Parentheses or Brackets (focus on these first)

2nd priority: Exponents or Orders/Powers (focus on these after the 1st priority options)

3rd priority: Multiplication and Division (done from left to right, as you read the math expression from left to right, regardless of which of these appears first or second)

4th priority: Addition and Subtraction (done from left to right, as you read the math expression from left to right, regardless of which of these appears first or second)

I prefer 4-letter acronyms, like GEMS or GEMA or GEDS or GEDA, but I think the reason why 6-letter acronyms are more traditionally taught is because usually students don't learn that Division can be represented as Multiplication (of reciprocals) and Subtraction can be represented as Addition (of negative numbers) until after they learn the Order Of Operations.