I confirm the long brilliant white plume here is from the solid boosters, whose exhaust is much hotter and contains tons of alumina.
A hydrogen engine gives a very pale violet plume from hydrogen, in atmosphere as in vacuum, nearly impossible to see. Pictures at Wiki. Nothing blue, nothing brilliant.
One exception is the RS-68 engine with a non-expected hydrocarbon-like yellow plume. I suppose it stems from the ablative heat protection in the lower nozzle, maybe some phenolic resin.
In the upper atmosphere, you may see a condensation trail like behind an airliner. In vacuum, maybe as well... If a part of the water freezes to a cloud. I don't remember seeing any at the Shuttles. It would be very diluted, hence observable only from a good distance.