Both use the same models, but they feel very different to use. A chat companion is an open window; an interactive story has a stage, a plot and stakes. Here is how to choose.
Start FreeStories give you direction but less total freedom. Chat gives you freedom but asks you to supply the momentum. SagaForge is story-first, with character creation for the freedom part.
Yes, within a story. You reply however you like; the scene keeps the conversation anchored.