I'm still deeply confused about Gemini as a product. Am I supposed to be using gemini.google.com or aistudio.google.com? The latter seems far more powerful but

I'm still deeply confused about Gemini as a product. Am I supposed to be using gemini.google.com or aistudio.google.com? The latter seems far more powerful but the former obviously has the more canonical URL. When I use the AI on my phone it says it's Gemini but it's most certainly not the same Gemini I see at gemini.google.com so what is it? When I ask my crappy little Google speaker something or press the microphone button on my Android Auto-equipped car why do I still deal with a comically bad "AI assistant" from 13 years ago instead of Gemini which seemingly has capabilities far beyond that of the assistant. Why can't Google get this right? When I use the chat bot at aistudio it is clearly the state of the art - at least as good as any other option - so why can't Google sort out the product discrepancies?