Hi The simple answers is yes, they're synonyms. So you're right in suggesting they are the same thing. However, the more complicated answer is that whenever you look at a list of possible synonyms and decide which one to choose there is often a deeper process connected to how informal/formal, and how commonly used, a word is. I wouldn't say that 'achievement' is less formal, but it is more commonly used than 'accomplishment', therefore the decision to choose the word 'accomplishment' possibly suggests a bit more care has gone into choosing the word, and this choice possibly reflects the sense that an 'accomplishment' has a greater value. So it's a bit of a 'grey area', but on the whole I'd say 'accomplishments' are worth more than 'achievements'.

The Cambridge Learner dictionary definitions distinguish them slightly: Achieve = to succeed in doing something good - usually something difficult Accomplish = to succeed in doing something good. https://dictionary.cambridge.org/us/dictionary/learner-english/accomplish

Nothing is the same.. everything that is similar has slightly different meanings/nuances/uses.. but sometimes it requires a lot of thinking about, like this one! lol