Tool AI generally refers to a type of AI which is used as a tool by the creators which gives them suggestions, but doesn't actually do anything in the real world, rather than being an agent with its own action and goal-seeking behavior. Something like Google Maps, which uses AI to plan the best route, but which doesn't drive your car for you.
This is meant as opposed to something like "agentic AI", where the AI has a goal and can plan and will take actions by itself to reach its goal.
https://www.lesswrong.com/posts/bSwdbhMP9oAWzeqsG/openai-s-sora-is-an-agent
A new Lesswrong post which argues Sora could theoretically be used as an agent by asking it to do something like generate Minecraft videos along with a keyboard and a mouse diagram, and if Sora is capable enough, it'll simulate the keyboard presses and mouse movements accurately, then you can copy the output, or something like "generate a video of a human painting", then replicating the movements made in the video.
I'd argue it's definitely not an agent as it can't continuously take actions to further it's long term goals. It doesn't quite fit the definition of tool ai that you provided as it doesn't give suggestions, it creates "content". It's in the same category as other generative models that make images and music.