They're separate options. Expertise is its own thing, trading up to +/- 5 points between attack and AC. You can do both, and in a round you don't really care about hitting (like a Warblade trying to recover maneuvers to use next round), it's often quite handy to do so.
Now, this means that anything (weapon, feat, class feature, etc...) that gives you a benefit when fighting defensively doesn't work for expertise unless it explicitly says so. If you wanted to houserule letting expertise count, I'd restrict it to an expertise of +/- 4 or higher, since that's the attack penalty of fighting defensively. If it were expertise of any amount, a quaterstaff fighter with cautious trait and Quickstaff weaponstyle feat would gain +4 AC from a -1 expertise penalty.