There are two different versions of Lightroom, both of which are current and both of which still receive regular updates.
One version, called simply Lightroom, stores images primarily in the cloud. There's also an option to store a copy of the cloud-based files on a local hard drive, but the "masters" are always in the cloud. The Lightroom desktop app is available in the two most commom subscription plans (the Lightroom only plan and the Photography plan).
The other version is now called Lightroom Classic and is the latest iteration of the traditional version of Lightroom that was introduced around 2007. Classic primarily requires images to be stored locally on hard drives (though it's also possible to have reduced resolution copies of them stored in the cloud)....the "masters" are always locally stored, however. Lightroom Classic is available in the Photography plan.
So you have options. If you have chosen the wrong option, I'm sure Adobe customer support will be happy to switch your subscription to the plan that you want.