Gemini is the name of both a model family and Google’s AI assistant. When you open the Gemini app, you use a ready-made service with an interface and features provided by Google.
Gemma is a different family of models. These have open weights and, depending on the version and equipment, can be used in your own solutions or run locally with a suitable tool. Their terms of use are explained in Google’s documentation.
The difference is a little like visiting an established café versus getting access to equipment for your own kitchen. Both can be useful, but they ask different things of you as a user.
You do not need to choose a side. A ready-made service can be convenient for everyday questions, while an open model can be fun to explore in a project of your own. Keeping the names apart makes the news a little easier to follow.
Source: https://ai.google.dev/gemma/docs