Case and Operation are wholly different in either military or medical terms and the differences are broadly the same… in English, anyway. I merely guess the same is true in German.
A military Case is a scenario, a what if question, a thought experiment if you like… and exactly the same case that academia or commerce refer to in case studies. The details and the reasoning behind them are explained in more readable detail in Leon Uris’ novel, O’Hara’s Choice, than many another source.
Military Case Boojum might propose that Snarkian forces invade Tovia, and ask what the Slithies could do about it. Surrender? Fight them in the Wabe? Launch a counter-attack on the Borogroves? Perhaps as a last resort, unleash the Jabberwock, with eyes of flame?
When the brass hats at HQ decide this, that or the other Case seems too realistic, they see what the boys in the back room might have to say about it, and tell them to draw their plans against it, surely and rather quicker than slowly.
Plan A - or B or Z - will include any number of suggestions and when any of those is crystallised into a specific task, that will be written up in immense detail as an Operation… a prime example taking us back to Germany where Operation Valkyrie was designed as an Operation which might be needed to counter any Case of breakdown in civil order in the Nazi state.
Part of the difference between theoretical Cases and actions in response to them is hi-lighted by the fact Valkyrie was intended to ensure the government maintained control of civil affairs in the face of, for instance, Allied bombing of German cities or uprisings of the millions of foreign forced laborers in German factories. By contrast it was famously used in an effort by Nazi-loathing Germans to ensure the very government which had designed it lost the control it was intended to guarantee.
Nevertheless, a Case is a study of theoretical events; an Operation is not just the Plans but the putting into practice of the Plans designed to respond to that Case.
Almost irrelevantly, between the two stand military Exercises, which are general training or practice for specific Operations.
Apart from any of that, it strikes me as very, very odd that any language could translate Case and Operation into the same word and I’d be asking for a third opinion, at least…