I can answer on the USN/USMC side.
Depending on the level of training (Primary, Advanced, FRS/RAG, Fleet, Advanced schools/Qualifications (MAWTS/TopGun/NVG/Low Altitude Tactics and Training).
I was an FRS/RAG IP and Fleet IP/Stan guy so I'll take a shot at those.
In the FRS/RAG (fleet aircraft initial training) - there are your standard Instructor Pilots. Within each phase (Air-ground, Air-Air, FAM, etc...) there are Standardization Pilots who give training to the IPs in each stage. If I remember correctly - all IPs could give instrument checks to students, but only a few could give the NATOPS checkride. The guy who administered the NATOPS qualification to the few IPs who gave NATOPS checkrides to students were the NATOPS Standardization checkpilots.
Fast forward to the fleet. Basically the same responsibilities for the INstrument chekers and NATOPS checkers. The standardization roles being at the MAG (Marine Air Group) level rather than at the squadron level and going on up through the Wing and higher.
Tactically at the fleet/squadron level - different instructor qualifications came with your different qualifications - section lead, division lead, NVG IP, LATT IP, ACTI/SWFTI quals, etc.... This is one area that although you might not have been an *instructor* in a primary, advanced, or fleet training center - I would emphasis instructor experience in whatever role you instruct - even if it was only as a SME at the squadron level giving training to fellow squadronmates.
This same tactical level training applies to the higher level of training schools like MAWTS and TopGun who have their own levels of IPs, Stan/Eval, etc....
For the USAF folks - this is similar to the IP/EP quals correct. IP = instructor pilot and EP = evaluator pilot (checking the IPs), and STAN fits in there how...making sure the IPs are all teaching IAW the regs/stan?