How does the IP address differ?

I would be interested in the IP address differs when I go on the laptop instead of using wireless internet with mobile hotspot.

No, she does not deviate.
The internally assigned IPs in the LAN which are done for the connection between the device and router via WLAN will not be routed to the Internet.

The IP for the WAN connection remains the same, no matter which device connects to the Internet via a router.

Assuming both devices are on the same network, then you are going to the Internet via the IP address of the router or modem, which is the same in both cases.

Yes, if I use the Wi-Fi, but if I use the hotspot function on the phone and use these applications that require Internet access then this would have to change, could theoretically with hotspot anywhere in Germany use the Internet

If your mobile phone hotspot has dialed into the mobile network and not in your WLAN, then the visible to the outside IP address diverges. If your mobile dials into the WLAN, you have not reached an IP change.

Tip: give it a try and then call

https://www.wieistmeineip.de/

to see which IPs you have out there.

Now I understand your question.

So with "Handy Hotspot" you did not mean that you connect the phone via USB and then use it as a modem or "WLAN card".

But: You make a connection with the mobile phone to one of the open hotspots and then use tethering / the mobile as a WLAN AP to connect the laptop with it.

Have I understood that correctly?

Then you have another IP in the network, but this is still understandable connected with you → for the hotspot you have to use access data. These are clearly related to your person → so you can understand what you have done.

The original question if you have a different IP than if you go via your own router via WLAN online: Yes. The IP of the hotspot differs from the IP of your WAN connection.

You can also check that easily. For example on this page here:

https://www.wieistmeineip.de/

Simply connect via WLAN and then in the variant that you are connected via tethering and mobile.

That's exactly what I wanted to know, thank you for the detailed answer!