Bard isn't a model, it's a product. Bard was launched with PaLM originally, the same model that the one employee claimed was sentient. At Google I/O they announced PaLM2 and switched over to Bard being backed by it, while also making Bard open to the general public on the same day.

Google is currently in the process of training Gemini, which is positioned to be their GPT-4 killer, as it's multi-modal, and presumably quite a bit more powerful than GPT-4 is. PaLM2 is more analogous to GPT-3.

NotebookLM is a very different product than Bard. Bard has a vague understanding of the information on the internet, and NotebookLM will, presumably, have some level of understanding of your personal documents. It will almost certainly be using PaLM2 until Gemini is ready. That will be neat because Gemini will be able to look at images and read visual charts in your documents. PaLM2 is only able to comprehend text.