"Cloud" is a word which is now used for everything and anything. you know, it's part of these words, like "AI" that are good to put in your portfolio, because it sounds cool.
Now, "in theory", and if "properly used", a shared hosting , is when a given physical server, is hosting several sites/clients. The resources (CPU, Memory, Disk, Bandwidth) are "shared" between all the sites/clients running on it. A "good" host, will have setup a system of quotas, to guarantee each client a given amount of resources, preventing a bad neighbor to consume everything. In practice, things are more or less like that, and often, having a bad neighbor (a site/client running on the same server as you), can cause performance downgrades.
A "cloud hosting", as said, can be all kind of things, but the idea is that, instead of relying on a physical server, we speaks about "virtual" server, the host (supposedly) runs several physical servers, and allocating their resources to provide the service. The system being more complex, it "should" offer better guaranteed resources. Also, a nice advantage of cloud hosting is that, (in theory), a host can allow you to upgrade or downgrade your package, on the fly, without having to reinstall/copy things, and without downtime. Like for example, they can allocate more or less CPU cores to your package. So it "should" be flexible, and able to adapt the budget based on your needs, and allow you to grow (or shrink) as your business evolves.
Personally, I would avoid "shared hosting", which by the way, are often over sold. It might be okay to host a static site, or very little site, which is not important, or to experiment.
Cloud hosting sounds good because of the flexibility , but I am too old-school, and only trust dedicated servers :) My server, my CPU, my RAM, my disk, knowing where my data are, and taht I am the only one to be able to access them... and my problems :)
Because of the nature of the cloud hosting , data can be stored "elsewhere", and accessed remotely , which with some hosts can cause lags.
In between, you can also consider VPS, which is like shared hosting, but with a lot less clients on the same physical server, and with real isolation , so your resources are guaranteed (still with "good" hosts).
Someone with more knowledges, and younger might add more useful information :)
