Managed hosting, is web hosting that is, to some degree, managed. Often, this is by the hosting company itself (a premium product), but also, we at Silicon Dales will effectively manage hosting on behalf of our WordPress and WooCommerce clients.
Managed hosting will generally include an element of software updating. Web hosts, particularly those which host WordPress, however, are providing machines containing lots of “software”. We have server’s Linux (and whatever OS or distro is installed) to update, PHP to configure, Apache (with or without Nginx), MySQL (or perhaps MariaDB), opcode caching, http accelerators, and a whole lot of other things in the “stack” to consider.
Very few “managed hosts” will take responsibility for your application, too, like your WordPress installation, and your plugins and theme files. Though some do perform automatic upgrades on WordPress (for example WP Engine) as well as some firewall and security services as well.