Can anybody know when I'm using hotspot instead of wifi on my iPhone?

Ah, that is a very useful bit of information. Yes, you can certainly use the hotspot on the other phone to connect to the internet. Again, if someone looks closely enough at the screen of your phone and knows what they're looking for, they would be able to see the hotspot icon in place of the WiFi icon. Other than that, they would have know way of know how you were connected to the internet.

What you're asking is a bit confusing. WiFi (or cellular) is how you connect your phone to the internet. The Personal Hotspot feature is how you use your phone's data connection to connect some other device (a computer, a tablet) to the internet. So, you don't connect your phone to the internet using the Hotspot feature.

A network administrator with the tools, knowledge and access to monitor a given WiFi network could tell whether or not you are connected to it. If you don't want someone to see you connected to a WiFi network, use cellular data).

If you need WiFi for an app to work, you need to use WiFi. The Personal Hotspot feature on the phone cannot connect the phone to the internet. It connects other devices to the internet.

If someone looks at the screen of your phone, they could, if they looked closely enough and knew what they were looking for, see that the phone was being used as a hotspot to connect another device to the internet.

Glad we finally got to a meeting of the minds!!