Under the DP-series classifications, just the cards that say "Trainer" are trainers. Supporters and Stadiums do not count as Trainer cards. Pokemon Tools do count as Trainer cards.
Just note this just stops Trainers being played from the hand. It doesn't stop the effect of existing trainers in play.
If older cards (pre-DP) say "Trainer" on it, it refers to Trainers, Supporters, and Stadiums, since they were subcategories back them. For example, Vileplume ex's Poke-Body stops regular Trainers as well as Stadiums.
