While characterizing Large Language Models (LLMs) solely as "next-token predictors" describes the autoregressive mechanism used during inference, it provides an incomplete mental model of how modern models function. During pre-training, models indeed perform next-token prediction by increasing the probability of tokens that appeared sequentially in the training data. However, post-training techniques, specifically Reinforcement Learning with Verifiable Rewards (RLVR), fundamentally shift the objective. In RLVR, the model explores novel sequences rather than imitating existing data; instead of predicting an "actual" next token from a dataset, the model adjusts parameters to make explored sequences more likely based on the rewards they earn. This distinction is illustrated via a chess analogy: a next-move predictor mimics grandmaster patterns, whereas a reward-maximizing engine selects moves to optimize win probability through exploration. Similarly, techniques like Reinforcement Learning from Human Feedback (RLHF) shift the model's objective from data imitation toward simulating helpful assistant behavior. Consequently, while the token-by-token emission loop remains identical, the underlying encoding evolves from mere statistical imitation of data to the maximization of rewards and the discovery of information through exploration.