Through some stores, I noticed that some are using an app that creates a new checkout page. Like for example this store: https://bit.ly/2Z7Ck3k
The checkout is totally independent of shopify, and in the case, when an order is placed, it is inserted in the shopify panel, and there it is registered that it was entered through the App.
Where is the documentation that teaches how to do something like that?
Rather than clicking a tracked URL just expand it using an added + on the bitly url:
If you look at the url structure it is using /a/secure. This is an app proxy url so would guess that this skips the checkout entirely and uses some custom app version. Payment processing would be handled elsewhere, and orders pushed into Shopify using the Orders API. Not going to go into risks/drawbacks with that method but this should give you some technical grounding for the how.
App proxy doc page: