If you choose Lightroom Classic, it’s based on local storage, so you must store your originals on your computer or on storage attached to your computer; your only storage limit is how much drive space you can afford to buy and back up. You have the option to sync limited resolution versions (Smart Previews) of your originals to the Lightroom Photos server in the cloud, so that you can use and edit those images in the Lightroom app for mobile devices.
If you choose Lightroom, it’s based on cloud storage, so you must store your originals using the Lightroom Photos server in the cloud. If you run out of space on your subscription plan, you can get more by paying a higher subscription fee. Lightroom doesn’t have as many features as Classic, and can’t print. But if it’s important for you to be able to see and edit any photo you have at any time on any device, you always have a great Internet connection, and you rarely print, Lightroom (cloud) might be a better choice.