Always check the rental car website to see exactly what vehicles they consider in those categories since there is no standard on how things are named. Most of what you and I would consider 'midsize' the rental companies call 'full-size'.
And what the manufacturer calls compact, rental companies call, "Full size," nowadays.
That being said, assuming it's an apples to apples (e.g. Ford Fusion and Ford Edge, or Ford Focus and Ford Escape) the room inside is functionally identical. True truck-based SUVs nowadays are basically the Ford Bronco, Chevy Suburban, Ford Expedition, Jeep Wrangler, and a few derivatives - the rest are all just crossovers, AKA station wagons with a lift kit (not meant derisively, I like mine a lot!)
That being said, rental companies lie much more about SUV size than they do sedan size, because the newer boxier back means that you can theoretically cram more suitcases into it, and suitcase capacity and number of seatbelts are how they measure things on their website. For instance, standard SUV is most likely a Ford Escape or Chevy Equinox, both of which are compact station wagons, while a full size car is the substantially larger Toyota Camry, Ford Fusion, or Chevy Malibu, with half a foot or more legroom and hiproom in the back.