All Cloud software (Photoshop etc) installs locally and can only be run on the computer on which it is installed and activated. You activate the software for use on a maximum of two computers at the same time.
You cannot run Cloud software remotely so you cannot log in to, say, a hotel computer or a friend's computer to use your Cloud software if the software is not installed on it..
The "Cloud" component is only the licensing. Adobe stores your Cloud membership details remotely on its servers and periodically checks your local computer against their membership records stored remotely to ensure that you're financially current.