Equivalent Rewards, Unequal Interfaces: Reward Coordinates in History-Conditioned RL

History-conditioned reinforcement learning agents use rewards both to define an objective and as inputs for online adaptation. Does preserving the objective also preserve adaptation? We distinguish objective, information, and policy-interface equivalence, and study their separation using interventions that alter only the rewards visible to the actor. Across five independently trained AMAGO policies in each of two continuous-control task families, positive-affine reward transformations alter actions and original-task returns. HalfCheetah exhibits a non-monotone, training-coordinate-specific response; Ant-Fwd-Back reproduces closed-loop sensitivity and a direct, reversible reward-to-action pathway. Teacher-forced replay localizes effects before environmental feedback, while HalfCheetah activation patching identifies structured, action-relevant changes not captured by the decoded task axis. Recurrent RL${}^2$ agents also exhibit strong coordinate sensitivity, whereas Decision Transformer controls show weaker sensitivity consistent with their weaker reliance on trajectory-specific reward evidence. Zero and donor interventions further connect coordinate sensitivity to reward reliance. These results demonstrate reward-interface dependence in learned adaptation: equivalent objectives and information need not produce equivalent behavior when reward is part of the policy interface.