I first did not notice any difference, but now when I opened it and noticed that I cannot change the color of the text in Slideshow Caption. This version seams to be the one which has the option to go to mobile. I guess it is registered in CC and I have not upgraded to that version. The other version is Lightroom 6 as a stand alone. This has my name written in the upper left corner and has no link to Mobile.
Any I idea where I should start to look this issue?
I guess it is registered in CC
Instead of guessing, why don't you actually look up the Lightroom version number of each one, and then we'll all know. Go to Help->System Info and report the Lightroom version number for each.
I don't know how you can open a CC version if you haven't subscribed to CC, as the free trial would only last 7 days.
Are you opening Lightroom via two different methods? How do you open Lightroom each time?
Please open the Lightroom CC version and sign out. Take a look at this article How to convert a Lightroom CC trial to Lightroom 6
Also, Let us know which version of Lightroom did you bought?