All three of the lamps are the same orange-red when on power, but with a tesla coil, I could see that one is a deep neon red color, one is a slightly more pinkish color, and one is almost white.
Why is this so? My guess is that the concentration of neon is less. But what is the weird white color gas? It isn't purplish like argon. (irl the color is much more like a daylight fluorescent, slightly bluish. But not the color of argon I remember from starters.)

Although all are called Neon lamps, it’s very rare to find one that’s actually pure neon.

The early general lighting / indicator glow lamps were usually made with 25% helium in neon.

Later, it was learned to decrease striking voltage by using about 0.5% argon in neon, often still with helium.

Later still, tritium or radioactive krypton-85 were added to avoid ignition delays in completely dark rooms.

High brighness types were achieved by raising the voltage, usually by adding mercury vapour.

Finally, the flicker types usually contain a substantial quantity of nitrogen.

On top of these compositional variations the gas pressure can also be significantly different.

All of these things have an influence on the discharge colour.

Joining LightsAreBright here with same question, see in his video :
https://www.lighting-gallery.net/gallery/displayimage.php?album=lastcom&cat=0&pos=37&pid=261171

Why is the difference in color between when the lamp is powered normally (at full power, between the electrodes) vs from an external HV probe (at low power, capacitively through the glass)

I dont expect anything like vapor pressure differences etc in a lamp which contents dont have to evaporate and runs at very low power in both cases ?