I have created a very simple app with with App Studio which only has a personal Tab which includes 2 websites to display. Nothing else. This 2 Tabs display a basic SharePoint site from within the same tenant. Deploy and installing the app works fine.
Now the problem is that the websites not always get visible. If you click on that specifc tab sometimes the websites loads but sometimes it stays just grey. There is no specific schema when it will work.
The cursor is always spinning, regardless of visibility. I'm confident that if i grep the traffic with wireshark that the teams client is doeing something. The world on the right site displays the website correct in the browser. The reload button again does something, cursor is spinning.
Adding a website tab on the other hand just embeds the URL you provide in a web view. it cannot communicate with Teams, and there are no expectations on behavior.
Essentially you can not just add any URL to a custom tab in app. You have to customize that page to work as part of an app. Please take a look at the Add Tabs to Microsoft Teams.
@Trinetra-MSFT thanks for the response. That helped to understand the difference.
Now it is a little bit clearer. So for example if i want to create a custom app with a tab that contains a website the SDK should be included in that site. And later of course I have more possibiliets to interact with that page.