The 'Y' in YF stands for prototype according to the 1962 Tri-Service aircraft designation systemTri-Service aircraft designation system. The 'F' stands for fighter, so YF stands for prototype-Fighter. These aircraft are operated by the US Department of Defense (USAF or USN).
The 'X' series'X' series is the name given for the aircraft operated under the NASAstrictly experimental aircraft; i.e. they are not prototypes.