BMW uses several. Are they interchangeable? Probably.
This is the original spin-on filter for the K100, K75, K1100, R1100, K1200, R1150 and R1200C. Commonly used alternatives are the Purolator L10241 and the Fram 6063 (these are not recommendations). Requires BMW tool 11 4 650.
For R1200GS/RT/S/R/ST, K1200S/R/GT, F800GS and F650GS Twin. Requires BMW tool 11 4 661.
For F800S/ST. The 541 filter has been an acceptable substitute for this filter, and the same engine in the GS line uses the 541 instead. I suspect it is as simple as the silver motors getting a silver filter and the black motors getting a black one. However, they are not the same filter. Requires the same 11 4 661 filter wrench as the 541 filter.
Available from BMW as tool 83 30 0 495 448, this is Hazet tool 2169. 74.5mm, 14 flats. Similar tools are Snap-on PW7614, Assenmacher H2175 or a typical #2 cup wrench. Drag Specialties and many car tool resellers can supply this. However, longitudinal (original) K motors, the OD must be less than 82mm, which some aftermarket tools are not.
Available as part 83 30 0 401 554 this fits filters with 76mm OD and 12 indentations. Nippy Norman's sells one. Marc Parnes and Jesse luggage sell wrenches which will work on both filter types, but neither accepts a 3/8" socket.