- Bard is that talkative text interface, a product.
- Gemini is the LLM design that currently backs Bard (but also other Google AI products).
- Gemini "Basic", Advanced and Ultra are different sizes of that design.
This is conjecture, but "Ultra 1.0" probably indicates that they intend to release more models based on the Ultra configuration. Since that's the most commercial of theirs, I wouldn't be surprised if that comes with some stability promises (e.g. Ultra 1.0 is still available when Ultra 3.0 is released, so that if you do your own validation when integrating in your own project, you can expect small-to-no shifts in the underlying model)