First, Gemini is just a better sounding name than Bard.
And then, few users are going to care about the difference between the model and the app that lets you use the model.
If Google kept this distinction they would have inevitably had to either come up with a new name for a new model, which would be needlessly confusing (when is something a new model would get tricky at times), or just call all models Gemini, again for little utility to users.
Now they can just call all the generative AI Gemini and be five with it. Bard becomes the Gemini chat interface. Duet is Gemini integrated into docs. The Gemini model can just get version numbers.
It's much simpler and nicer sounding to boot.