So there is a lot of confusion about these terms, many people incorrectly use the two terms interchangeably.
Both a cloud server and a VPS are virtualized servers.
Both can have either shared or dedicated resources.
Both may come with a nice web interface.
Both may allow for many customization options.
However, there is a clear and simple distinction between a cloud server and a VPS server:
In a VPS, if the physical node (server in a cluster of servers) goes offline, there is no redundant node that the cluster can fail back to. This is a catastrophic failure that means your website will be down until the physical node is repaired in the data center. Sometimes this can be resolved quickly, but I have seen it take days.
In a cloud server, if the physical node hosting the server goes offline, then the web server will be automatically transferred to a working node in the cluster. This is also called High Availability. A properly built cloud server hosting provider might also have redundant nodes in a completely different data center in another part of the world so if a natural disaster like a hurricane happens, and it shuts off all power in Miami FL, your server could be transferred to a data center in Germany with only a few minutes of downtime while the transfer happens (this however is mostly only for very large enterprise clients and most cloud server providers will not go to this level of redundancy)
This makes a cloud server not just a better option then a VPS, but also it might be better than a dedicated server if having a web site with minimal downtime is the goal.
It is possible to build your own cloud server cluster with at least 2 dedicated servers however. So it depends on how much resources you are willing to spend.
Ultimately, it will come down to price, what you are comfortable in doing, and if you feel like you can trust your hosting company to do all that they can do to reduce possible downtime. A lot of this will depend on your use case, estimated traffic, and other such factors. My advice is to find something that can be customized exactly the way you need it to be, and then if your website grows, easily upgraded at a fair price.