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But, technically, a pitcher being used to pinch-hit or pinch-run is a PH or PR, unless they stay in the game to pitch (very unlikely).

The pitcher who is already in the game will have to hit in the spot of the player that the DH is replacing. The wikipedia entry is actually not too long:

The designated hitter can be moved to a fielding position during the game. If the DH is moved to another position, his team forfeits the role of the designated hitter,[7] and the pitcher or another player (the latter possible only in case of a multiple substitution) would bat in the spot of the position player replaced by the former DH. If the designated hitter is moved to pitcher, any subsequent pitcher (or pinch-hitter thereof) would bat should that spot in the batting order come up again (except for a further multiple substitution). Likewise, if a pinch-hitter bats for a non-pitcher, and then remains in the game as the pitcher, the team would forfeit the use of the DH for the remainder of the game, and the player who was DH would become a position player (or exit the game).

Unlike other positions, the DH is "locked" into the batting order. No multiple substitution may be made to alter the batting rotation of the DH. In other words, a double switch involving the DH and a position player is not legal. For example, if the DH is batting fourth and the catcher is batting eighth, the manager cannot replace both players so as to have the new catcher bat fourth and the new DH bat eighth. Once a team loses its DH under any of the scenarios discussed in the previous paragraph, the double switch becomes fully available, and may well be used via necessity, should the former DH be replaced in the lineup.