What is the difference between Install and Activate on the Themes page?

They are two separate steps:

• Install adds the theme to your Installed tab. Nothing on your storefront changes.
• Activate switches your live store to that theme.

To switch:

1. Go to Settings → Appearance → Themes.
2. On the All Themes tab, click Install on the theme you like. Once installed, the same button turns into Activate.
3. Click Activate (here or on the Installed tab).
4. A pop-up warns that your current theme will be replaced. Click Save & Activate to keep a copy of your current design under Your Saved Themes, or Cancel to stop.

The active theme shows an Active badge and its name appears next to the page title.