In March of 1944, several German s.Pz.Abts. were busy fighting the Soviets, and losing badly. Memoirs of the 4th Tank Army commander Lelushenko tell of "72 tanks captured, including 49 Tigers". Now, one can claim cases of misidentification, but in this case, journalists did their job well. Photos taken on March 13th definitely show a number of Tigers.
Photo from the Uman captured and destroyed vehicle collection point.
So, as you can see, these Tigers clearly exist. Let's look through claims of losses from the German side. S.Pz.Abt 503, 507 and 509 were present in the area around March. Let's see how their accounting went:
The 503rd claims to have lost 2 vehicles on March 9th, and 8 more up March 29th. The 507th reports 4 lost vehicles in all of March. The 509th reports 5 vehicles lost in all of March.
Wait, what happened? That's less than 20 Tigers lost in all of March, when the Soviets have over twice that in the first two weeks, with photographic evidence! Where did they come from? The answer lies at the end of the month. On March 30th, 24 losses are recorded, 21 of which are marked as "destroyed by their own crew". The fact that these vehicles have long been photographed at Soviet collections points makes that claim doubtful.
There you have it, some creative accounting in how and when a vehicle counts as destroyed, and you end up with an invincible fighting force! On paper, at least.
In contrast, let's take a look at how the Soviets did it.
Here we have some losses from various causes (artillery fire, mines and explosives, aircraft, unrecoverable losses, technical losses). Look at that technical losses field! The numbers are huge! 84 tanks lost to artillery fire in total, compared to 468 breakdowns? That sounds hard to believe. Thankfully, the description clears things up.
"The technical losses field also includes vehicles stuck in mud, even for a short time, and tanks requiring repairs, where one tank could undergo several repairs, and count several times. Tanks needing medium or heavy repairs are also counted. As a result, the amount of losses is larger than the total amount of tanks."
There you have it, the two sides treat losses radically differently. Soviets can count one tank as lost multiple times (the same tank can also be "built" multiple times, if a hull is shipped back to the factory for refurbishment), while the Germans don't count the tank as lost at all until they are sure that they cannot reclaim it. Who knows how many Tigers were recovered, repaired, and sent into battle again, never counting as a loss until meeting their final resting place on the battlefield.
These, and many other examples, readily demonstrate that one must always be cautious when comparing numbers written down by different organizations, as similar terms often carry vastly different meanings.