I'm still not getting it. Is it that the crossover has a smaller third-row window, less cargo space, and less practicality? :looks puzzled:
A crossover is a SUV built on a car platform.
They tend to have a more upright seating position than a car, more ground clearance and suspension travel than a car, are more likely to have available AWD, and typically have more rugged styling than their hatchback, station wagon, and minivan counterparts. (The larger ones also tend to have a lower roof than their minivan counterparts.)
The US has a
legal definition used to determine whether a vehicle is a sport utility vehicle (that some of these vehicles marketed as "crossovers" fail to meet, but most do), based on being "capable of off-highway operation", which is determined by it either having 4WD (including AWD) or over 6000 lbs GVWR, and it meeting four out of five criteria based on ground clearance and angles. (There is also a "small sport utility vehicle" class for vehicles that are 2WD and under 6000 lbs GVWR, but meet the other criteria... but unlike the other sport utility vehicles, they're legally considered cars.)
Myself, I look at the height as a clue, as well. If it's under 60" tall, it's probably just a hatchback/wagon that's had ruggedized styling, even if it's being marketed as a crossover (this is a common trend in the "subcompact" crossovers popular nowadays, especially those from luxury marques). If it's over 65" tall, and it isn't a van, it's probably a "real" crossover. In between... could be a tall hatch (think vehicles like the Honda Fit and Ford C-Max) or wagon (think the Toyota Prius v), could be a small crossover (things like the Kia Niro and Hyundai Kona).
(And the heuristics for "van" often include things like "does it have a short nose" and "does it have sliding doors".)
This is also why some people call the Model X a minivan. It doesn't have the ruggedized styling of most crossovers, and it does have a short nose and, while not sliding, weird doors. However, it doesn't have the shape of a minivan in the third row (for aero reasons), but it's following a trend in luxury crossovers that are marketed as "sport utility coupes" by their predominantly German manufacturers. (This is compounded by a trend in automotive enthusiast spaces, to call three-row crossovers "denial minivans" or similar - they're being used as a minivan, their owners would often have been better served by a minivan, but minivans have an "unsexy" stigma where crossovers somehow don't, so they buy a crossover.)
Also, smaller crossovers tend to have a tall hatchback form factor (that is, with a small rear cargo area), whereas larger crossovers sometimes have more of a tall wagon form factor (often with a third row in the cargo area).