What are the different types of Extensions in SharePoint

If you are talking about SPFx extensions than, there are 3 types of SPFx extensions:

1. Application Customizers: Adds scripts to the page, and accesses well-known HTML element placeholders and extends them with custom renderings.
2. Field Customizers: Provides modified views to data for fields within a list.
3. Command Sets: Extends the SharePoint command surfaces to add new actions, and provides client-side code that you can use to implement behaviors.

Please refer this Microsoft document link for more info.