This https://www.macmillandictionary.com/dictionary/british/according-to explain the first meaning of "according to" as: "If you do something according to a plan, system, or set of rules, you do it in a way that agrees with or obeys that plan, system, or set of rules"
And https://www.merriam-webster.com/dictionary/in%20accordance%20with one explain "in accordance with" as: "In a way that agrees with or follows (something, such as a rule or request"
Does "according to" cover the meaning of "in accordance with" ?
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1- She always did everything according to the rules. (https://www.merriam-webster.com/dictionary/according%20to)
1a- She always did everything in accordance with the rules. (Is this version acceptable? Does it mean the same thing as the original one? )
2- The soldiers said they acted in accordance with his orders. (https://www.merriam-webster.com/dictionary/in%20accordance%20with)
2a- The soldiers said they acted according to his orders. (Is this version acceptable? Does it mean the same thing as the original one? )
In the kinds of contexts you mention, they mean roughly the same, but I would say that "in accordance with" is slightly weaker, or allows more leeway, and can suggest that rules or orders were not actually broken, rather than that they were followed, if that makes sense. "in accordance with" also has a slightly more formal feel. In other contexts there can be a more substantial difference.
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In the kinds of contexts you mention, they mean roughly the same, but I would say that "in accordance with" is slightly weaker, or allows more leeway, and can suggest that rules or orders were not actually broken, rather than that they were followed, if that makes sense. "in accordance with" also has a slightly more formal feel.
In other contexts there can be a more substantial differenc