Why do some IAPs lack an Intermediate Fix and/or include other fixes between Final Approach Fix (FAF) and Intermediate Fix (IF)? I have noticed that some Initial Approach Procedures (IAP) do not mention an Intermediate Fix, but they do include at least one fix before the Final Approach Fix. Take, for example, this IAP of the JFK airport. It includes a Final Approach Fix (MATTR) but the one that precedes this (CORVT) is not labeled as Intermediate Fix. Is it always implied that the fix before the FAF is the Intermediate Fix? Another example is this IAP, also of JFK, where JAMCA appears to be the Intermediate Fix but, nevertheless, is not labeled as such.

In addition, there are some IAPs like this which neither include an Intermediate Fix, nor have the last fix (in this case, CEMUG) labeled as FAF. In this particular example, RUSHY, instead of CEMUG, is labeled as FAF.

Is there any rule which I am not aware of and that will help me clarify the above cases?
The rules are quite lengthy -- a 509 page PDF.  They're all spelled out in excruciating detail in the FAA Order 8260.3D, United States Standard for Terminal Instrument Procedures commonly referred to as the TERPS.  

It's available for download here.   

I would suggest researching your questions there, and returning here if you have a specific question regarding the application of the TERPS.