difference between 1w and 3w led

After looking down the barrel of a lot of box store cree xre lights I notice there isn't really a size difference in the die of 3w and 1w lights.
So my question is what makes a 1w a 1w and 3w a 3w light?
Is it material,type of wire or somthing else. I am talking about the led itself.

the boosting of the shop
there once were differences between Luxeon I and Luxeon III led
(even when a good part of ppl think that there is no difference at all. The III were just the few "better" ones Luxeon was able to produce ((lower vf, better tint)). At the beginning both types were offered in the "good" tints, but quickly one leared the customers pay more money for better bins/tins, so suddenly there were no Lux I in neutral white any more. At least thats what I think)

with the XR-E (or the Seoul P4) there is only ONE model of the led.
If that description says "1 W" or "3 W" or whatever, that might be how hard the led is driven by the power device of the light
(but in most cases it will be a bad product! Better get something from a respected maker, You will be much better off)

Actually the determining factor is sort of the junction-to-pad thermal resistance. That establishes the limit on power level that meets the temp limit before it gets into the lower life/lower efficiency of higher temps.

But the die does have its own limits independent of temp. Isn't a larger die involved?