The -o models are "just" stronger versions of their non-suffixed predecessors. They are the latest (and maybe last?) version of models in the lineage of GPT models (roughly GPT-1 -> GPT-2 -> GPT-3 -> GPT-3.5 -> GPT-4 -> GPT-4o).

The o1 models (not sure what the naming structure for upcoming models will be) are a new family of models that try to excel at deep reasoning, by allowing the models to use an internal (opaque) chain-of-thought to produce better results at the expense of higher token usage (and thus cost) and longer latency.

Personally, I think the use cases that justify the current cost and slowness of o1 are incredibly narrow (e.g. offline analysis of financial documents or deep academic paper research). I think in most interactive use-cases I'd rather opt for GPT-4o or Sonnet 3.5 instead of o1-preview and have the faster response time and send a follow-up message. Similarly for non-interactive use-cases I'd try to add a layer of tool calling with those faster models than use o1-preview.

I think the o1-like models will only really take off, if the prices for it are coming down, and it is clearly demonstrated that more "thinking tokens" correlate to predictably better results, and results that can compete with highly tuned prompts/fine tuned models that or currently expensive to produce in terms of development time.