I use five KX-TGA681 with the base station KX-TG6821 (with answering machine), according to the manual (see link) it is also compatible with the base station KX-TG6811 (without answering machine). https://1drv.ms/i/s!ApPbK-so_LAXm5hIf7uGZdmMEe0lqg?e=JCErPF

no the station charges the device

They are simply different models with slightly different functions. The KX-TGA681EXB can be connected to a Fritzbox, but I recommend using an AVM handset, e.g. art. no. 5776809.