Configure 2 LANs with different classes or force AP to assign IP to his connected devices

You cannot have two IP classes as AP is not a router. There are combined devices router+AP, but I have googled the documentation for the AP model you mentioned and this one isn't. AP is more like a switch, so it's nothing strange that devices connecting to your TPLink get the IP address from Fritz's DHCP. They are all in the same subnet.

If you want some devices connect only to TPLink's WiFi, and others only to Fritz's WiFi, you have to use MAC address filtering. From the documentation it looks that both should support it. If you want for example some specific devices connect to Fritz, and all others to TPLink, add only MAC adddresses of these devices to the MAC address filter list on Fritz, and deny access to the same MAC addresses on TPLink. Then the specified devices would be able to connect only to Fritz, and all other devices would be able to connect only to TPLink.

Probably you can't do it the other way, because from what I see in the documentation there is no option to deny access to particular MAC addresses on Fritz, only allow. But you should check for yourself, the documentation may be incomplete.

Also, if you want fixed IP for some devices, you have to assign them on Fritz, as it is providing DHCP for the entire network, regardless of where the devices are connected. Or disable DHCP on Fritz and enable it on TPLink, if DHCP on TPLink is able to operate on both wireless and wired interface (you cannot have two DHCP servers in the same network segment).