It can be hard to make a distinction between the two, as many standard VPS are marketed as "Cloud VPS" merely as an attempt to capitalize on the popularity of the buzzword.
If one compared a VPS with an actual cloud server (a virtual server on a hypervisor spanned across a cluster of dedicated servers) there would be some obvious advantages of going with a cloud server opposed to a VPS.
The primary advantage would be that your data would be much more redundant. This redundancy means that drive failure or other catastrophe would not equal lost data. Now plenty of VPS are "backed-up" using RAID cards and multiple drives, but the on the cloud your data would remain available throughout the drive replacement as it would "float" over to another server within the cloud environment.
That's an excellent feature. But with every feature, there is an added cost. A true cloud server will cost a few times more than a VPS with similar resources. The only question at this point would be, "how important is that data?"
If your answer is "mission-critical," then you will want to do your homework and identify a reputable cloud server provider. But if not, a cloud would likely not be worth the added investment and a solid VPS will suffice.