Managed Hosting
Also known as: managed WordPress hosting, managed server
Paying somebody to run the server so updates, backups and security are their job rather than yours.
Ordinary hosting rents you the computer. Managed hosting rents you the computer and somebody to look after it.
For a shop with no server person, that second half is worth real money. The alternative is you becoming the server person at an hour you did not plan on.
Managed hosting is not the same as a hosted platform, and the words are close enough to confuse. On managed hosting your site is still your files and you can move them. On a hosted platform the site is the platform.
That difference is the whole ownership question, hiding behind two similar phrases.