I've just bought a d8, and noticed that the number arrangement is different from my other one. My new die has only even numbers on one half, and only odd on the other half. My old die has 1,8,5,4 on one half and 2,3,6,7 on the other.
Is there any correct pattern for it?
Does it make any difference?
There's no correct pattern, and in a fair die it makes no difference.
In practice, most standard dice sets are not entirely fair, because of how they're tumble-polished after removal from the molds.† How an unfair die is numbered can make it more unfair if the manufacturer decided to cluster all high (or all low) numbers near each other. Few manufacturers do this though, exactly for that reason—both your dice mix high a low numbers in each half, just in different ways.
However, the imperfect shape caused by tumbling affects the "rounder" dice more (such as the d20), and it's unlikely for a d8 to suffer noticeable unfairness.
† Due to demand for fairer dice, manufacturers such as GameScience and Chessex make dice that haven't been tumble-polished.