Yes, the actual LLM returns a probability distribution, which gets sampled to produce output tokens.
[Edit: but to be clear, for a pretrained model this probability means "what's my estimate of the conditional probability of this token occurring in the pretraining dataset?", not "how likely is this statement to be true?" And for a post-trained model, the probability really has no simple interpretation other than "this is the probability that I will output this token in this situation".]
[Edit: but to be clear, for a pretrained model this probability means "what's my estimate of the conditional probability of this token occurring in the pretraining dataset?", not "how likely is this statement to be true?" And for a post-trained model, the probability really has no simple interpretation other than "this is the probability that I will output this token in this situation".]