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 ?

I think it has something to do with the field strenght gradients VS which gas ionises easiest. That color becomes dominant where the field strenght is highest.

In both cases the field is by far not uniform inside the lamp. In both cases the discharge cloud borders on the places where the field is not sufficient to ionize the gas. Why we don't see regions of the 2 really different colors at least in some of the operating modes ?

It would be interesting to see how the lamp with the purple glow reacts if powered from line voltage with additional high value resistor (something 20K...100K Power rating 3W for 20K, 0.5W for 100K)

It would be interesting to see how the lamp reacts to the HV probe while being also powered from line voltage with the high resistor - But here you must be careful, to not trigger a flash over the resistors with the HV, which would then damage the lamp with the line voltage. An arrangement of few resistors and an MOV will make it safe to test

@Ash True, at 2:42 in that video you can see the difference. I see no color difference when the lamps are plugged in, i.e. mains voltage through electrodes. Only when lit up externally by that mini tesla coil

Also another interesting thing in the flicker lamp (third one). The ionized gas is white-ish in color, but when I touch the glass, there is a small spot of red neon glow there. Here are some images:

I think that this is similar to a plasma ball the case with you flicker flame lamp.
Also: The tesla coil drives the lamps at HF, which may cause the argon or other gases or impurities in the lamp to become ionized.

Cant tell from the picture if it is really Red discharge, or your fingers skin color illuminated by the Purple discharge giving a reddish color

What if instead of touching the lamp with hand, you touch it with a conductive object painted in black ?

Also, there may be quite some UV emission here. Put some fluorescent colored paper or something near the lamp and see how it reacts to the line voltage vs. to the HV discharge

In the first picture, a fluorescent orange plastic disc is kept, but it didn't glow bright. (I did test the orange disc under BLB and it was bright)
In the second picture a black metal piece is touching the lamp, and a spot of red discharge is seen (neon).


In the separate picture, a fluorescent yellow sketch pen cap is kept, which is also not glowing bright.