The word describes how a vehicle is put together, not how large it is or where it can go. A crossover starts as a passenger car: one welded unibody shell, front-wheel drive as the base layout, a transverse engine or a flat battery floor. It is then raised, given more suspension travel and usually the option of all-wheel drive. The Kia Niro at 4,430 mm and the Volkswagen ID. Cross at 4,153 mm are built exactly that way.
Almost no manufacturer uses the term in its own advertising, and that is the honest state of it. They say SUV, and this site tags cars the way their makers describe them, so treat crossover as a note on engineering inside the SUV category rather than an alternative to it. Where it matters is ownership. A car platform means car ride, lower weight and better economy, along with real limits on towing and on ground that a ladder frame would shrug off.