It's easier to start at the beginning.
Ilford sold a developer called ID-20 a Universal MQ dev mainly used for prints, when they began commercial production of Phenidone they reformulated ID-20 with it instead of Metol (early 1950's), there were complaints about shifts in image colour abnd variations in warmth, so they added Benzotriazole to control this the new formula was ID-62. These where powder developers.
PQ Universal is a liquid concentrate, the Sodium carbonate is replaced by Potassium carbonate and Sodium or Potassium Hydroxide to allow far greater solubility & concentration.
However with the introduction of the third generation Multigrade papers in the 70's PQ Universal was found to give different warmth depending on the filtration/grade used so a new developer variant Multigrade was introduced, my experience is it's quite warm toned with warm toned papers.
PQ Universal is great for film processing, especially when highly dilute, Ilford no longer give all the data that was once available in the past. The Multigrade dev is specifically marketed for papers but it'll most likely work for films as well, concentrations differ.