I think they are just different designs with different use cases in mind. I use Safari tab groups and find them very helpful to quickly get back to specific work contexts, sort of like just separate browser windows that I can close and bring back as needed.

Having only used Chrome's tab groups briefly I think I recall them being more of an ad-hoc organizational tool for existing tabs in the window. In that case, I think Chrome's tab groups are closer to the name, whereas Safari tab groups are a separate concept that could have maybe used a different name.