The Online Store is the default sales channel when you have a store. However, a sales channel app is not about the online store. It is anything like a POS app, eBay or Etsy, in game purchases and anything you can think of elsewhere where you can sell your goods.
The Checkout API will work for such sales channels that you interact with or create, but will not be capable of completing checkouts on your default Online Store sales channel - that is only possible via Storefront API up to a certain degree (the last checkout step is always a completion step URI which cannot be completed via API).
Only public apps are able to use the Sales Channel SDK and thus the Checkout API. A public app need tot be published though.
Best wishes!