Simpson's paradox: analyzing trends per subgroup can give a different result than pooled data.

Berkson's paradox: analyzing a single subgroup selected with a function aggregating two traits (additively?) will indicate an anticorrelation between the traits.

Simpson's paradox says you can't judge group trends from subgroup trends. Berkson's paradox says given a group selected in a specific way, it will have a certain property in itself. They're just different statements.