I know that ATC have their own radar, but radar isn't an IFF kind of thing, it just shows a blip that something is there. How do you differentiate between military and civilian aircraft with just a blip? Do Military aircraft even show up on a TCAS? If they aren't using ADS-B then I think that answer would be no. Actually, NEXTGEN shares data with TCAS so a blip from a radar could be shared with civilian aircraft I guess.
ATC has basically 4 types of radar, long range, terminal (at an airport), ASDE and secondary radar, commonly known as the beacon radar or IFF or ATCRB if you want to call it that. The ATCRB is a type of radar operating on 1030 and 1090 MHz. The aircraft has to interrogate this radar. This radar on the ground includes Mode-S. All this Mode-S essentially does is provides more info about the aircraft like the type of aircraft. Each aircraft that has Mode-S has a unique Mode-S identifier which is programmed into the Mode-S transponder.
I think ADS-B is an entirely separate system but I'm not sure since it came out after I left Flight Inspection Ops and avionics maintenance and I don't handle any mobile/aircraft ADS-B systems in my job now with the FAA.
TCAS operates on the same 1030 and 1090 MHz frequencies but is mainly aircraft to aircraft. It operates separately from the ATCRB radar. To accomplish this there is a data buss on the aircraft referred to ARINC 429. There are 2 types of ARINC 429 busses, fast and slow. On this buss when the transponder/ATCRB transmits it sends a word telling the other 1030/1090 MHz systems not to transmit. The TCAS does the same thing.
The primary radar indeed just basically sends a pulse out and receives a reflection from anything it hits. This reflection could be aircraft, cars, big birds or weather. If you were to look at a controls radar screen for each aircraft at the radar facility you would see those marks, the skin paint from the primary radar and just a bit farther out the ATCRB return. By the way the primary radar return isn't a "blip" but a line on the screen.
Once the primary radar and the ATCRB receive it's return the info goes into a computer, at 1 time called the common digitizer, which turns this analogue info into digital info so it can be sent to the ATC radar room. At that point more computer magic happens and the data tags, which contain the call sign, speed ATCRB setting (squawk code) altitude and more are added to the "blips" and then out to the controllers screen. I'm not sure if ATC can add a data tag to an aircraft that isn't using an ATCRB. But now it is almost impossible to even get close to a major airport without a ATCRB in the aircraft. I guess if the aircraft were out in the middle of no where, like the west, you can have very few problems flying around with a ATCRB transponder.
At one time if a controller didn't see the primary return and just the ATCRB return they could not provide radar info to the aircraft. I do know of at least 1 FAA facility that has a waiver for this requirement.
As for your question about how different military "blips" differ from civilian "blips" they don't. Both the primary radar and the ATCRB returns look exactly the same. The only difference is in the computerized tags added by the system at the radar control facility. AND the tags for all aircraft are identical in the fact that they have the exact same type info on the tags. The only difference is the info shown in the radar tag.
And yes both military and higher end civilian aircraft have TCAS. I don't know if every military aircraft have TCAS BUT with just the ATCRB return to the TCAS system will create a target on the TCAS indicator.
I remember when I was still flying with FAA Flight Inspection myself and 2 pilots went to Atlanta to pickup a new aircraft. It had 1 of the 1st TCAS systems installed in FAA aircraft. Just to see it work is pretty cool.
Hope this explains a bit about FAA radar.