Hello,
The questions that you are asking, them self are really vast to explain in few paragraph. I suggest you should spend some time with Google, read few detailed articles explaining these in details.
However, I shall try to put an overview.
VPS → Virtual Private Server
Cloud → Shared Hosting
As you may see, the idea behind VPS is giving you a virtual machine. Same as your laptop or desktop PC, but its virtualized. So Processor / Discs / RAM are separated from anyone else and you are the only users of that resource. You get to choose your own OS and Software that you can to install on that barebone virtual computer.
You have the option to highly secure them, just like you can do with your own physical hardware with multiple lever of authentication and layers of data encryption & so on.
In case of shared hosting, others with their code / files will be present on your same disc and processor pipe or RAM, plus server admins may have the rights to access your files. Here, you don’t get to choose, configure or deploy software or OS and do deep modifications of these software as per your need.
Technically speaking, yes they can see. Matter of fact they always do for copying your entire VPS on multiple separate hardware server for fail safe.
However, seeing and reading aren’t same. Since you can encrypt your virtual disc at OS lever and then further layers of encryption data with application that you are using, its pointless for these service providers to even try reading your data.
So its safe to say that you can trust any of these big names.
None of the links you have provided are service offered by any country. These are private companies based on a particular country. They are taking advantage of certain country and their data privacy laws where raw data may not be shared with law enforcement unless some explicit court order.
However, this is geared more towards businesses like Google / Facebook / Dropbox and such. For individual user VPS, even if someone gets your virtual disc, its extremely difficult to read inside that disc with layers of encryption.
Try any big names
AWS / Oracle / Microsoft / Google
Digital Ocean / linode and so on.
More or less they all follow similar privacy policy and offers similar software solutions (VPS → Disc level encryption and so on)
I don’t know what you are trying to host, what is making you so serious about data safety, but in case its something highly classified, I guess you should hire software consulting firms for your setup.
As otherwise, data privacy and security are in anyway the core philosophy behind all these technologies you talked about, so for average joe, things are well covered.
Thanks.