I've always wondered why the different services use different refueling systems?
There is only one service that does it differently and that's the Air Force yet they all started out doing it via probe and drogue. It was SAC that needed to evolve to the boom because the B-47 and B-52 were found to be extremely hard to tank via probe and drogue and they needed higher transfer rates that the boom could provide. During the transition period, tankers like the KB-50 and KC-97 could provided probe and boom tanking (respectively) for USAF customers and the F-105 was equipped with a probe and and boom receptacle so it could tank from either one or the KC-135 that replaced it. Probe and drogue is by far the most widely used method worldwide.
F-105 could refuel using probe or boom
The F-104 was last USAF fighter to use probe method
In case of emergency, it's silly to have a Navy A/C not able to take fuel from an AF tanker because it doesn't have a drogue. Any thoughts?
Yes and no. We had an aircraft in extremis during Desert Storm get vectored to a USAF tanker and when they got there...lo and behold, it was a KC-135 equipped with boom only. We always tried to talk to tanker or confirm with AWACS that tanker had a basket. The KC-10 was first modern Air Force tanker that did it right with a boom and separate basket so it could handle USAF or USN/USMC/Allied/Coalition customers. Some KC-135s were modified with podded basket systems solving the problem. One would hope the replacement tanker would also follow suit.
KC-10 using drogue for RAF Tornado and waiting F/A-18s (with boom retracted)
KC-135 with wingtip drogue refueling pods in addition to boom