With a usual Ahrefs subscription you will only be able to use OpenApp.
Each monthly package (Lite, Standard, Advanced, Agency) contains certain amount of OpenApp API rows.
There are two cases when you can use OpenApp:
1) as a user, you can use one of the OpenApp applications developed by our partners.
By using any of these application, OpenApp API rows included into your monthly subscription are consumed.
2) as a developer, you can build your application using our API and then submit and sell your app to thousands of our users.
If you need API data for your own internal needs or in-house application and want to make requests to Ahrefs API directly, you will need a separate API subscription.
The smallest API subscription comes with 500K API rows included and costs $500/month.