I found this tutorial which shows how to build an AdHoc IPA for TestFlight. But there is also the TestFlight SDK and I don't understand if I need this and why I would need this for a simple beta test distribution.
Can someone explain?
You don't need to. You can upload any proper ipa on their site via this page: https://testflightapp.com/dashboard/builds/add/
If you're having problem with your ipa, they have help here: http://help.testflightapp.com/customer/portal/articles/402782-how-to-create-an-ipa-xcode-4
The SDK is only for features like tracking crashes, session reports, etc. It's quite nice, but by no means required.