Sorry for the late reply but I've been away.
There is only one definition of resonance - that where the reactive component of the impedance is zero. That is true for ANY AC circuit - including antennas.
But you're correct in that it might not matter much. While a 3:1 SWR will cause transmitters to cut back, it's only a 25% power loss or about 1.25db. When you consider 1 S-Unit is 6db (ideally), that's about the width of the needle on many S-meters. Nothing noticeable except in the most extreme conditions.
No, a 1:1 SWR may not occur and won't in most antennas. But don't count on the lowest SWR being at resonance - in fact, very few antennas will have a 50 ohm impedance at resonance without some type of matching network.
