If you use the company’s app or website they see and save everything you enter, but you do often get more features beyond just chat. If you download on your computer it’s all private but m more effort and sometimes less features

You're forced to use way smaller models because you don't have the necessary RAM/VRAM (basically very fast memory) to store the largest model after it is read from your (much slower) hard drive. So the model has less parameters (basically a lesser amount of knowledge) and won't perform as well, especially for more complex tasks. It's also likely to be slower. You can download updated versions of the model with ollama once they're released.