The phrase "a completely different case" is correct and usable in written English.
You can use it to indicate that a situation or example is entirely distinct from another one being discussed.
Example: "While the previous example illustrates a common issue, this is a completely different case that requires a unique approach."
Alternatives: "a totally different situation" or "an entirely separate matter".
I must say I find that a completely different case.
"Brodsky was a completely different case: a genius of a different order.
This study was done in a major urban trauma center and their recidivists were more susceptible to penetrating trauma, all-terrain vehicle/motorcycle collisions and possibly bicycle accidents, which indicates a completely different case mix compared to our study.
In 2012, involving a completely different case and scenario, an admittedly corrupt member of the New York Legislature ("the Legislator"), who was, herself, tied to a number of criminal episodes, apparently persuaded the federal prosecutors prosecuting her case (or was persuaded by them) to wire her home.
"They're all completely different cases," he said.
A similar yet completely different case of online video-diary-keeping comes courtesy of Lance Stephenson, a junior at Lincoln High in Coney Island, which is best-known for producing the troubled Knicks star and sneaker entrepreneur Stephon Marbury.
Our fine neighbor's past record of having some of the worst air pollution in the country should not bear upon any judgment of innocence or guilt in this particular and completely different case.
We have included observations of case characteristics for several of the species but it should be recognized that Limnephilidae cases, even within a single population, can be very different, and some species rebuild a completely different pupal case in the 5th instar from that of the earlier instars.
In two completely different cases, the apparent broth viscosity of several consecutive strain generations was investigated.
The capability of the developed approach is illustrated through a case study where an optimization model is built and solved departing from other models focused on completely different cases at other hierarchical levels.
The paper maintained strict secrecy and even published a "spoof" first edition with a completely different front page in case I got hold of an early edition.
