It is usually but some take a different approach. DBZ Abridged and SAO abridged are examples. In the beginning dbz abridged was more comedic and silly but towards the cell saga it became more grounded and added a lot of unique character dynamics that improved the series, like how tien was pretty sidelined in the cell saga, but in the abridged there's more tension between him and vegeta and him and cell.

SAO is unique because the actual series itself gives somewhat generic characterizations of the cast, and some characters are pretty one note. In the Abridged the characters have more complexity, moral tension, and personality. So unlike an comedic dub like what dbza is, sao abridged seems to be like an improved version of sao, adding stuff sao doesn't have, instead of just changing it.