For the Luftwaffe it was 1 pilot; 1 kill (no shared victories). Kills on the ground didn't count either.
On the Western Front a 'point system' was only for 'awards'. Some confuse this with actual kill numbers (ie they will claim LW pilots got 3 kills for a bomber, which isn't true. They got 3 points but only counted 1 kill).
The point system in the west worked as follows:
Abschüße - Destroyed (out right shot down)
Single Engine Fighter - 1 point
Twin Engine Fighter / Bomber - 2 points
Four Engine Bomber - 3 points
Herausschüße - Separation (damaged a bomber so severely that it gets separated from the formation)
Twin Engine Fighter / Bomber - 1 points
Four Engine Bomber - 1 points
Entgültige Vernichtung - Final Destruction (finishes off a damaged bomber already separated from the formation)
Twin Engine Fighter / Bomber - 1/2 points
Four Engine Bomber - 1 points
Points were only used to determine 'awards'.
Iron Cross 2nd class - 1 point
Iron Cross 1st class - 3 points
Honor Cup - 10
German Cross in Gold - 20
Knights Cross - 40
The Luftwaffe term for 'Ace' was 'Experte' (Experten - plural).
On the Eastern front awards were given out based on 'number of kills'.
For example:
Iron Cross 2nd Class - 2 / 3 kills
Iron Cross 1st Class - 8 kills
German Cross in Gold - 30 kills
Knight's Cross - 45-50 kills
Oak Leaves to the Knight's Cross - 100-120 kills
Swords to the Knight's Cross with Oak Leaves - 200 kills
Diamonds to the Knight's Cross with Oak Leaves and Swords - 250 kills
After the pilot landed he would fill out a kill claim form. He would need to list witnesses (wingman, squadmate, ground observer, film etc...) This form along with witness statements and/or film we be sent on-high for review. It could take up to a year for a kill to be confirmed (LW kills from late 44 to the end were never confirm by RLM). Hartmann example lost (or had stolen) his second log book. Reconstructing his kill claims, let alone confirming them is currently all but impossible. This will lead some to conclude he is a liar or a creation of Nazi propaganda etc...
In principle the LW kill claim procedures were some of the most strict of WW2. In practice, especially towards the end of the war, this wasn't always the case.
As for book recommendations there would be so many to start. To understand if a particular pilot 'over inflated' his claims you would need a detailed biography.
Folks have claimed for years that Hans-Joachim Marseille lied about his claims yet these can be detailed in Shores and Ring's Fighters over the Desert (for example Marseille 17 kills in 1 day can be confirmed by the allied losses).
In the end what does it really matter if Hartmann only had 320 kill or Marseille only had 100? If the number of actual kills confirmed is lower then their total claims it doesn't necessarily mean they 'inflated' their claims. All though, for example, 4 pilots of JG 27 were discovered firing their guns into the empty desert by a LW recce aircrfat. These 4 pilots filled kill claims when they landed, so its been the realm of pssibilioty that some 'inflated' their claims. These 4 were discovered and split up and sent to different units.
Discrepancies can be found on the allied side (all sides for that matter).
For example the first LW kill claim by the 4th FG was on 15 April '43. (Don Blakeslee, a 190). No 190 loss can be found during this date.
Here's a brief summary of that days action:
According to the 4th Fighter Group history 'Escort to Berlin', there were two separate encounters with German fighters, about 50 minutes apart, involving two different squadrons. Officially the show was called Rodeo 204 -- a fighter sweep to Furnes, Belgium, to Cassel, France.
Times given are conflicting, probably because the group was split up. Both 56th and 78th Group aircraft participated to gain experience. At 1701 hours, Blakeslee was leading the 335th FS when he spotted three FW-190s over Knocke, at 23,000 ft., and bounced one from 6,000 ft. above. The summary says the German pilot dived away and the tail chase leveled off at 500 ft. before the Focke-Wulf crashed into the sea near Ostend.
Meanwhile the 334th FS was crossing the North Sea, and they engaged FW-190s at about 1750 hours. Two pilots were shot down and killed: Capt. Stanley Anderson (P-47C 41-6407)[and Capt. Richard McMinn (P-47C 41-6204). Both crashed into the water several miles off the coast of Belgium, between Ostend and Blankenberghe.
Lt. Col. Chesley Peterson was the overall mission commander Peterson's plane (P-47C 41-6414) was the first loss of the day, and not involved in combats. He aborted early because of engine trouble shortly after take-off, and bailed out into the sea 30 miles off the English coast. Rescued by a Walrus 45 minutes later
There were no 190s lost that day. 15 FW 190A-4s of II./JG 1 did engage in combat with P-47s. 14 returned unharmed and 3 kill claims, 1 190 was forced to land due to engine troubles before combat began. One pilot (5./JG 1 Ofw. Ernst Heesen) claimed 2 p-47s.
3 P47 losses (2 combat, 1 non-combat)
1 claimed unknown 190 by Blakeslee. (observed crashed into the sea).
There's no need to get to caught up in kill claims, after all that is all the so-called 'kill totals' represent is 'claims' from that time frame.