The name hassio was replaced, almost a year ago, by the name “Home Assistant OS”. If you refer to the official documentation, you won’t find any reference to the old name.
There are four ways to install Home Assistant in order to provide users with more choices to suit their needs. They are described in the Installation documentation and compared in a table (at the bottom of the page). Another comparison is provided in Community Guides: Home Assistant Installation Methods
The recommended installation method is Home Assistant OS because it contains additional functionality that makes it easier to administer the system. The remaining three types all require the user to know how to install and manage the operating system.