Regarding the transfer from an Internet service provider to another, the domain name is the only thing that can be transferred . The hosting can not be transferred because it refers to the disc space which the previous company has offered you, after buying a hosting service.
If you want to transfer your hosting of your website from one company to another, then you need to transfer the contents of your website that was hosted to your provider's disk drives in your new provider, by buying a new hosting package.
