I find that Solar RGB has higher red saturation compared to the Twinstar S, which is offset by the green spikes in the Solar RGB. Whereas Twinstar S has more reddish glow as a whole. However, Solar RGB has a narrow range of rendering - oranges and purples look much more reddish than under other fixtures. The Twinstar S doesn't have such an extreme effect despite the redder background glow.
This is likely due to the solar RGB only using RGB leds and no white, whereas the Twinstar also includes white LEDs in the mix, relying less on pure-green LEDs for lighting up near-green plants, and moving to a pinkish tint which seems to be popular for your LED fixtures and T5HO setups.
Plugging the solar RGB into the TM-30-15 (color rendition) spreadsheet shows that the colors are more vibrant, much less accurate than sunlight, and most orange/red-tinted tones are hue-shifted red, just as you observed.
For reference, this spreadsheet shows graphs of the spectral output, the Rf-Rg plot which is a newer interpretation of CRI that scores both fidelity (accuracy) and gamut (saturation). The third plot compares measured hue and saturation (red ring) to the reference (gray dashed ring). The last shows the overall tint of the light compared to an "ideal blackbody" or "pure white" curve.
There are no published measurements for the Twinstar S, but going from the 6500k specification and pictures of the individual LEDs, plus your pink-hue comment, I'm guessing it's a more red/pink focused light using RGB+W leds. Looking at the Rf-Rg plot, we see that it scores much higher on the fidelity (accuracy) axis, while still having the same gamut (saturation) as the ADA. This might help explain why the Twinstars are more versatile and popular for a variety of aquascapes.