You need to install a virtualisation layer on the top of the Operating System (OS), that layer is called: the Hypervisor. This is what divides the machine into slices.

(Un)fortunately not! The best ones are from Xen® and KVM®: which are both used by Amazon AWS® . A popular one is OpenVZ® (because it is cheap) but the quality of the Hypervisor is lower.
Competitors are so afraid that they all came together as a Consortium to develop: OpenStack®. But depiste all their efforts (and capital) they cannot catch-up.
Regardless of the best Hypervisor of the next 5 years: Amazon AWS® will allow you to switch/migrate very easily~.

VPS is the 🧙 ancestor 🧙 of the Cloud. So why remain on the previous generation of technology any longer??

The abstraction level is higher in the Cloud and you do not have to care about the underlying hardware: the provider takes care of everything. Just pick your needed resources and you are done! Your data is replicated automatically (achieving a 99.999% availability). The RAM & the CPU can be changed with a simple stop and start. You can copy/save/backup your entire disk (which is impossible on a VPS). Scalability is another big merit of the Cloud: as you can scale up your resources without migrating to another server. Instead of “VPS” the new terminology is: “instance” which refers to the Cloud.

VPS are becoming very cheap for two reasons:
- (more & more) unscrupulous companies oversell their dedicated servers, meaning that they create more VPS slices than they should (which will cripple the performance of each VPS) ;
- there is a supply surplus on the market, especially with old hardware or very cheap hardware like low-end Intel Atom® CPUs.

It has to be planned properly (to minimise downtime to the maximum, maybe 1-5 minutes). It also depends on what is running on your VPS. Only a human can do this (unfortunately). But once you are in the Cloud: you will be able to downgrade/upgrade your resources.

Simply because: it is the biggest and the most advanced. Customers already picked Amazon AWS® : they have around 50% market share. They provide solutions of any size from the Startup level to the entire Datacenter.

Traffic going into the Cloud is free: so if you are collecting, storing, or archiving data this is the best solution for you. Outgoing traffic is expensive but: nothing is really unlimited. By paying for bandwidth you now have the incentive to optimise your website, code, images, data to the lowest size possible. The biggest reward for this is a lightning fast website delivered to your customers as quick as possible.

As of today: people want uptime. Thus said, if you do not need uptime (are you sure?), the cheapest cloud provider is: OVH®, which is a French company. OVH® takes 2-4 business days to reply to any support ticket (even an urgent one). Before you go, please have a look at:
the Amazon AWS® status page
VS
the OVH status page 💩.