There are 4 versions of Lightroom;
Lightroom Classic with the icon LrC. This is where Lightroom began. It doesn't store your images. You import the images to it. The images are on your storage media. The catalog, a relational database, manages information of of your storage media.
Lightroom Desktop is basically photo browser which has a "Cloud" and "Local" area, tab.
The Cloud browses photos that have been added to the Adobe Cloud.
The Local browses photos in connected storage media, internal, external.
Lightroom Mobile is you phone, table or similar device. There are 3 major areas. Gallery, Android, for photos taken by your Mobile device; Lightroom which is photos in the Adobe Cloud; Community which is images shared by the Adobe community.
Lightroom Web that you can access on any browser by accessing "lightroom.adobe.com" and signing is to your Adobe account. All items in your account. All images in your adobe account that have been added to the Adobe Cloud are visible.0