A "crossover" is the industry term for what amounts to a station wagon with SUV-like styling.
"Minivan" and (non-"crossover") "SUV" are two names for what amounts to a station wagon built on light-truck frames -- with originally somewhat different demographic targeting in the marketing, but eventually the "SUV" class's marketing broadened to subsume the target that minivan marketing had been focussed on -- originally to fit loopholes in passenger safety and efficiency regulations (which have since largely been closed, hence, the emergence of the "crossover", which was a reversion since the expense of the regulatory dodge was no longer particularly useful.)
"Minivan" and (non-"crossover") "SUV" are two names for what amounts to a station wagon built on light-truck frames -- with originally somewhat different demographic targeting in the marketing, but eventually the "SUV" class's marketing broadened to subsume the target that minivan marketing had been focussed on -- originally to fit loopholes in passenger safety and efficiency regulations (which have since largely been closed, hence, the emergence of the "crossover", which was a reversion since the expense of the regulatory dodge was no longer particularly useful.)