An offensive task force strategy is used when the fleet is attacking, while the defensive strategy is used if the fleet is under attack.
Design types have no bearing on target selection. There's some sort of hard-coded analysis that categorizes the ships along the lines of the types in the strategy settings.
I don't understand why this (crucial) part of the AI is hard-coded, while most of the rest of the game is so easily moddable... Maybe because it could be exploited?