There are several types of web hosting: shared, VPS, dedicated and cloud.
Shared Web Hosting
The most common (and usually the cheapest) type of web hosting for people who just want to quickly set up a web site without spending a lot of money. Shared web hosting involves renting out space on a web server that’s shared with other customers much like living in a dormitory with other coeds. For both shared web hosting and shared living arrangements, no one person bears the full cost of energy, Internet access, upkeep, etc. If a roommate that’s hogging the Internet bandwidth by download some massive update for Windows, while playing games online and streaming music and video on their TV...there won’t be much bandwidth left for everyone else who depends on it. Similarly, a popular or demanding web site may compromise the performance of other web sites sharing the same web server.
A demanding roommate may be forced to look for their own apartment and the same is true for web sites that share a server. If a web site is too demanding to run along side many sites sharing the same machine, a web hosting provider may ask its customer to upgrade to a virtual private server (VPS) which is basically like an apartment.
The customer can choose an apartment that is big enough to meet their needs.
A virtual private server is similar to shared hosting since you are one of many tenants in a building (server). But you have much more freedom. Shared web hosting limits your ability to install certain kinds of software. But with a VPS you can do anything you would with your own computer.
There are two types of VPS services: managed and unmanaged.
A managed server is like a nice apartment building with a concierge and other amenities. There is always someone available to answer questions and address needs.
An unmanaged server is like a no frills apartment building with really cheap rent. But that doesn’t necessarily mean you need to live in a bad neighbourhood. It just means you need to be more self-reliant. There’s no one on hand to help you. There is no concierge or security cameras to protect you. And there is no handyman available for repairs. The landlord will make sure the water flows through the pipes and the lights stay on, but you are responsible for the upkeep inside the walls of your home.
An unmanaged VPS works largely the same way.
If you run into a problem (e.g. your website gets hacked) a technical support agent may try to offer guidance, but they have no obligation to help you.
Managed vs Unmanaged
If you take two VPS plans with identical specs, the managed hosting service will generally cost $20-$30 dollars more than the unmanaged service.
An unmanaged VPS can be as little as $2.50 per month--and that's the standard price, not a sale price or new user promotional offer. A VPS can be an incredible bargain for anyone willing to deal with their tech issues on their own.
A dedicated server is a physical computer with one renter. You do not share a dedicated server with others. But you can run multiple web sites (and other services--FTP, e-mail, etc.) on a single machine.
Usually when renting a dedicated server, you will be given a list of available machines and their specifications--including their CPUs. It can be a bit difficult to compare one CPU to another. Also, newer computers continue to offer more power at lower prices, but once you are locked into a rate for a dedicated server the price tends to remain flat; whereas the cost of VPS and cloud servers fall as computers become cheaper and more powerful.
Generally, you shouldn't really get a dedicated server unless you have a good reason.
Basically, cloud computer/hosting refers to any service that offers virtually unlimited server capacity.
Some providers like Amazon Web Services (AWS) can handle anything you throw at them and pretty much will never crash due to an unexpected traffic surge. But that means your server bill can rise unexpectedly. And if you server/software is poorly configured somehow, you costs can be needlessly high. Other cloud providers like Digital Ocean allow customers to create as many servers as they want and instantly increase (or decrease) resources for any given server. This does not happen automatically. If your server gets a sudden surge in traffic you need to adjust your server(s) as you see fit. This means your site can crash if it receives more traffic than it can handle, but you can quickly remedy the problem without before forced to pay for something you don't necessarily need or want.
The "cloud" is a just a marketing term and there's no way to quickly distinguish one kind of cloud rovider from another.