What is the difference between 決して～ない and まったく～ない?
There's definitely an overlap in the "completely/absolute" domain between 決して...ない and まったく...ない
If we want to split them apart, then Chocolate has a good pair of sentences to help illustrate the difference:
= definitely don't forget.
決して usually relates to volition or decisional completeness / finality.
Or the opposite of not being committed to remembering.
Command-related usage is quite common for 決して so it also has a kind of 必ず sense.
=I don't understand at all
Or we could say there's nothing in the contents I understand (the opposite of understanding all of the contents).
まったく relates to completeness of things.
A further signal other than looking at usage that tells us 決して is more formal is that 決して depends on the 音読み of 決 whereas まったく when written in kanji uses one of the 訓読み of 全.
They basically mean the same thing, except the latter is more informal.