The online store is entitled to its own application
You can now go to the App Store or Google Play Store to download the Nintendo Store application. On it, you can directly purchase your games by connecting your Nintendo account (and your credit card), and not just digital games since you will also find physical editions and Nintendo products, accessories to consoles.
It is also on this application that you will find articles surrounding the eShop, while consulting your activity on Nintendo machines, even the 3DS and Wii U. If you wish, you will also be notified when sales are active, particularly on games placed in your wish list.
It’s an additional application to that of the Nintendo Switch App and that of Nintendo Today, which will not necessarily help to avoid any confusion. But if you want to buy a game via your smartphone, it will now be (a little) simpler.