A minivan is basically a taller wagon and an SUV a jacked up wagon. The perceived differences are mostly marketing.
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Your kidding right? The amount you can carry in a Van versus wagon or even an SUV is quite a bit. As I said the Wagon is a decent option and better than a hatchback and more agile than an SUV but it has compromises.
"The 2016 Toyota Sienna has
39.1 cubic feet of cargo space behind the rear seats,
87.1 cubic feet behind the second-row seats and
150 cubic feet with the third row folded and the middle-row seats removed, which is easy to do."
You can carry your buddies, bikes, and camping gear in a Van pretty easily. Good luck doing that in a Wagon or even SUV. And you get decent gas mileage on the highway. Privacy in van is pretty obvious. You can't peer into a Van as easily as anything else.
Like I said the Wagon is decent for smaller applications, like a quick trip to the beach with board but it just doesn't cut it for trips that need much more space. Volvo has a history with the Wagon but don't expect that many companies to follow suit.