Training vs. inference
Training is the one-time (expensive, slow) process of teaching the model by showing it data and adjusting its parameters. Inference is every single time you actually use the model - fast, and it doesn't change the model at all. Nothing you type to Claude or ChatGPT teaches it anything permanent; your conversation just disappears from its "brain" the moment it ends (unless a product layer saves and re-feeds it, which is a separate thing).
Training happens in massive data-center runs, often months long, producing a frozen set of weights that then gets deployed as "the model" (e.g. Claude Sonnet 5). Every time you send a message, that's a fresh inference call - the model reads your whole conversation as input text again from scratch, predicts a response, and forgets. This is why "memory" features in AI apps are really just re-inserting your past messages into the prompt every time, not the model actually learning.
Have a long conversation with Claude about a fact you invented (e.g. "my dog's name is Ziggy"). Start a brand new chat and ask "what's my dog's name?" It won't know - proving the model itself didn't learn anything; the previous chat's context simply isn't there anymore.
You tell Claude your dog's name mid-chat, then open a brand new chat and ask again. What happens?