As others have noted, tent only doesn't necessarily mean tent only. In any case, let me pass along that a truck camper is an RV at Yellowstone. At least, that's what they say if you call and ask. That goes for the roads as well.
On the other hand, Washington State Parks allow any type of camper to use any type of spot as long as you fit. In this case though, it's hookup vs nonhookup for the most part. Their online reservation is pretty clear.
Maybe, some other websites are clear for other places you will visit.