Lightroom CC 2015 is the Creative Cloud version.
Lightroom 6 is the standalone version. Both are sold by Adobe.
You can install both versions on two computers, CC can be installed on as many computers as you like, but you can only be signed in on two at the same time. Not sure of the details for the standalone version, but you can definitely install on two computers.
New features are only available in the CC version - the standalone version will not have these features until LR7 is released.
The standalone version only receives updates in the form of support for new cameras.
Both versions are installed locally on your computer, and your photos will be on your computer. The term "Creative Cloud" is somewhat misleading.
Simple answer is Yes you can install all Adobe products on 2 separate computers that are used by the same person but not at the same time. So you can have any and all Adobe products installed on a Desktop and a Notebook, 2 Desktops or 2 Notebooks, one at work and one at home and or 1 at work or home and one for traveling. But the Restriction comes in that those 2 systems can't (Shouldn't) run the same Adobe program at the same time. Although I have done that for certain reasons without anything bad happening.