Adobe also has different icons for LR Classic and LR (cloud). I don't use the cloud version but I believe the icon is just a box with "LR" inside. Classic is similar but the text is "LrC".
I had the same problem with CS5. I found it easier to just spend the 10.00 a month to get everything up to date with the PS online. Yo don't have to download everything it has but you can and you can choose not to put your stuff in the cloud