As shown in the figure, both bulbs are Philips HPI-T 2000W with the same batch, but why are the halides inside the arc tube different in color?

On the left it looks like normal crystallization after cool down, on the right one it seems to be remelted, because last time it was operated for very short time, so just partially warmed up (only to partially melt the condensed fill salts but not enough to evaporate them).
Next power cycle and both will look different again.

This means that this difference can be eliminated if both bulbs are sufficiently preheated.

Or they may both look completely different as well.
The apparence of the condensed salt used to vary after each time the lamp runs and then cools down. Mainly the first 100 hours (or 10 cycles) or so when new, or even after position change.
It is part of tye reason, why all the optical output performance (lumens, CCT, color quality) are rated after the lamp has been operated for 100 hours, as the form where and how the halides get settled influences where the molten salt pool reside and so what temperature it will have, so what pressures of tge various arc atmosphere components will be during runtime. So ithas to settle to its moreless stable position first. Sometimes the pool uses to reside in the lowest spot due to gravity, which does not have necessarily to be the coldest spot (where it may condense, but the liquid then may be dragged by the gravity to some lower spot).

Or they may both look completely different as well.
The apparence of the condensed salt used to vary after each time the lamp runs and then cools down. Mainly the first 100 hours (or 10 cycles) or so when new, or even after position change.
It is part of tye reason, why all the optical output performance (lumens, CCT, color quality) are rated after the lamp has been operated for 100 hours, as the form where and how the halides get settled influences where the molten salt pool reside and so what temperature it will have, so what pressures of tge various arc atmosphere components will be during runtime. So ithas to settle to its moreless stable position first. Sometimes the pool uses to reside in the lowest spot due to gravity, which does not have necessarily to be the coldest spot (where it may condense, but the liquid then may be dragged by the gravity to some lower spot).

This means that the metal halide content inside each lamp will be different when it leaves the factory, of course, I think the biggest difference in the color of the two bulbs is likely to be the difference in the amount of use of the two.

The content does not have to be different in any way. Even the same fill content will look different if it crystallizes in a different way. The exact temperature profile when cooling is what matters here...