Update index.markdown (home-assistant#11993)

* Update index.markdown

Updated verbiage to align with re-branding of Home Assistant and Home Assistant Core

* Update index.markdown

- edited links for installation
- cleaned up the upgrading section for clarity

* :pencl2: Tweak

* ✏️ Tweak

Co-authored-by: Franck Nijhof <[email protected]>

source/hassio/index.markdown

@@ -1,19 +1,19 @@
 ---
-title: "Hass.io"
+title: "Home Assistant"
 description: "Manage your Home Assistant and custom add-ons."
 redirect_from: /integrations/hassio/
 ---
 
-Hass.io turns your Raspberry Pi (or another device) into the ultimate home automation hub powered by Home Assistant. With Hass.io you can focus on integrating your devices and writing automations.
+Home Assistant turns your Raspberry Pi (or another device) into the ultimate home automation hub. With Home Assistant, you can focus on integrating your devices and writing automations.
 
 [Go to the installation instructions »][install]
 
-The advantages of using Hass.io:
+The advantages of using Home Assistant:
 
 - Free and open source
 - Optimized for embedded devices like Raspberry Pi
 - 100% local home automation
-- Easy installation and updates (powered by [HassOS] and [Docker])
+- Easy installation and updates (powered by the [Home Assistant Operating System] and [Home Assistant Core])
 - Management web interface integrated into Home Assistant
 - Create and restore full backups of your whole configuration with ease
 - Install many popular add-ons with a single click! For example [Google Assistant], encryption via [Let's Encrypt] and dynamic DNS via [Duck DNS].<br><br>[Browse available add-ons &raquo;][all]<br><br>
@@ -25,14 +25,13 @@ The advantages of using Hass.io:
 
 ### Upgrading
 
-Hass.io users can update Home Assistant via the 'Hass.io' panel in the UI. However, please note that Home Assistant updates take some time to roll into the Hass.io builds. Therefore, there is often a slight delay (a day or two) between the availability of a Home Assistant update and the update being available in Hass.io, so be patient. When a Hass.io update is available, it will be shown as a notification in the ‘Hass.io' panel in the web interface.
+Home Assistant users can update via the 'Supervisor' panel in the UI when a new version is released.
 
 <p class='img'>
 <img src='/images/hassio/screenshots/dashboard.png'>
-Hass.io dashboard with upgrade notification (under the hamburger menu -> Hass.io)
+Home Assistant dashboard with upgrade notification (under the hamburger menu -> Supervisor)
 </p>
 
-
 [Google Assistant]: /addons/google_assistant/
 [Snips.ai]: /addons/snips/
 [Let's Encrypt]: /addons/lets_encrypt/
@@ -41,6 +40,6 @@ Hass.io dashboard with upgrade notification (under the hamburger menu -> Hass.io
 [comm-add-ons]: https://community.home-assistant.io/tags/hassio-repository
 [all]: /addons/
 [chat]: https://discord.gg/K3UVxJd
-[HassOS]: https://github.com/home-assistant/hassos
-[Docker]: https://www.docker.com/
+[Home Assistant Operating System]: https://github.com/home-assistant/homeassistant
+[Home Assistant Core]: https://www.home-assistant.io/docs/installation/
 [install]: /hassio/installation/