What defines a "case" of COVID?
That might seem like a stupid question. But it's tough to put the answer into words.
Even among experts, there's widespread disagreement—as there has been since the beginning—on the definition of COVID-19.
The CDC technically does have a definition, as does the World Health Organization. But both are so broad and vague as to be of little use; academically rigorous but impractical to apply and inscrutable to most humans. Plus, out of date. Here's the WHO from 2020:

In the early stages of an outbreak of a new disease, it's not unreasonable to define "cases" liberally—erring on the side of catching as many as possible, and missing ideally none.
But as time goes on, a more nuanced system of definitions needs to be adopted. Now, as the world's news outlets enter a third year of their steady stream of reporting about cases of COVID being on the rise (or, occasionally, fall), most are actually referring to positive tests.
The endless repetition of "cases of COVID-19" implies that someone knows what this term now means, and that we're all referring to the same thing when we say or hear it. That miscommunication bleeds into everyday conversations. But, uncle Gene, did you "get COVID" or did you just test positive for SARS-CoV-2?
That probably sounds pedantic. Language is dynamic, and when it comes to the rules of what's grammatically "proper" I've always been at the anarchic end of the spectrum. If people understand what you mean, it's proper. But right now we really should be on the exact same page. Many professional communicators are still saying things like "cases of COVID are rising" when they mean "lots of people are testing positive." These are not the same thing.
A pandemic is one of those times when we all—especially journalists and government officials—really need to be on the exact same page about terminology. The terms we use in emergencies like this are materially important; they shape our perceptions of safety and risk, and subsequently how we choose to act and live our lives.
Yet, even two years into the pandemic, we're not on the same page at all. I realized it the other day when I made a comment on Twitter about how testing positive for SARS-CoV-2 does not equal a "case." Nor does it mean you "got COVID." People had questions, and I realized I should say more. Even though I don't have a great solution to the big question.

Everyone knows this (I hope!) but it bears repeating since our words are not reflecting that we do: SARS-CoV-2 is the virus that causes a disease called COVID-19 (or COVID).
The virus is the cause; COVID is the effect.
The two have never been interchangeable. With omicron, they are diverging further. Tracking the spread of the virus is important. But it's done in service of preventing the disease, cases of which are the metric of ultimate importance.
As you know, you can carry the virus and test positive without developing COVID-19. There's nothing unusual about that; it's how infectious diseases work, from flu to gonorrhea. You can carry influenza without getting sick. If you did, you wouldn't say you had a case of the flu.
This distinction is often made clear as it applies to HIV, the virus that causes AIDS. The disease is defined by a severely impaired immune system—not by testing positive for HIV. Most people with HIV do not have AIDS. Thanks to modern medications, many never will. In the 1980s, that wasn't the case. But as the two diverge in meaning, the distinction is even more important.
An analogous effect is playing out with the omicron variant of COVID SARS-CoV-2, especially in places where many people have been vaccinated. Enormous numbers of people are testing positive for SARS-CoV-2, but remaining asymptomatic. Maybe some sniffles and sneezes. This is absolutely worth keeping track of. But in medicine, a "case" standardly refers to a disease, not its cause. And it's extremely misleading now to say that "cases" of COVID-19 are skyrocketing when you actually mean lots of people have almost no symptoms.
This matters because COVID is a serious disease that demands to be taken serious. It's also misleading to imply that COVID is become a mild disease just because infections are less likely to lead to severe disease.
No definition of COVID will be perfect. People develop a wide array of different symptoms. But we need to and have a definition. Typically in situations like this (with diseases whose symptoms vary widely), the case-definition will be something like "3 of the following 9 symptoms for a period of more than 48 hours."
If you have a good idea for how to define this, please let me know. Comment or write me. I'll keep thinking about this. For now, I'll just be careful about language. I've surely used these terms (cases, COVID, SARS-CoV-2) interchangeably over the years, even though the misuse has always gnawed at me. But I resolve (belated New Years) to never let it happen again. If anyone else wants to do the same, it's an attainable resolution.