There is a difference.
The online storage can go offline, thereby being risky. Obviously no one wants that!
The vendor could go out of business. I don't want that!
Their disks could fail or their data-center could get hit by earthquake, power failure, their techies walking out, getting hired by competitors, their VC funding could get pulled, someone going berserk and causing criminal damage on their RAID arrays. Yikes! I for sure don't want that!
OTOH
The cloud storage is fuzzy.. fluffy.. and if you don't live in Seattle or Portland, it is related to feeling good instead of bad and depressed. I want that!
It is also related to fluffy white angels flying around waving magical fairy dust over all that ails humanity, so your data is always healthy and in a magical land. I sure want that!
It is also related to contents of a pillow so it represents cushioning properties. This means whenever there is any kind of bump, my data will be cushioned in a fluffy cloud and would be saved from any harm. If I'm an IT manager I will also sleep well at night thinking my data is not on a hard drive but on a soft pillow! So I want that too!
What happens behind the cloud is mysterious yet somehow I am hypnotically suggested to not even think to question or look inside it. I definitely never question, if it's stored on cheapest drives possible without any protection like, RAID or backups, environmental, power supply redundancies etc. etc. I simply avoid all these questions and the headaches they cause. O boy! I want that! As a result this also means more customers, lower costs and higher profits for the "storage provider" by just changing a label, so they definitely want that!
In summary, online v/s cloud = storage no one wants v/s storage everyone wants.
My personal view of this... Meanwhile, all of us techies (myself included) focusing immensely at discerning the differences in the wording of what are obviously synonyms due to common usage, busy looking for all of the subtleties, get to marvel and discuss and clarify and debate, deriving multiple types of cerebral highs in the process from inane stuff, as if our heads weren't already full enough with it. Of course, we want that!
Stackexchange gets to have more traffic even though the content borders on inane, hence incrementally more ad revenue. Is a no brainer that they want that! Note: on "no brainer" I am using the word inane, in it's more obscure reference i.e. about the brain and not no brain. On this, please do not take offense and instead give me your understanding. I want that!
Finally search engines get excited and all the machines kick in having more to link and sort and sift and index more keywords on many of their criteria. I bet they want that!
Seriously, if someone reading this actually gets to take a humorous or sarcastic or questioning look at what we are doing with our brains.. I'd consider that enlightening and I personally want that! :-)
Reference:
http://en.wikipedia.org/wiki/Cloud_Storage
http://en.wikipedia.org/wiki/Online_storage