You are correct in that there is rarely a single set of wheels that will work on both rough, rocky ground and soft sand, although many of us try! On the right are the pneumatic Hobie Trax wheels. On the left are the original (non-pneumatic) hard plastic or rubber Hobie wheels for pulling your yak over city streets, or on asphalt or concrete parking lots, and on some uneven hard or firm surfaces.
The Trax wheels carry what we (4-wheel drive enthusiasts) used to call "high flotation" tires in that with low air pressure they flatten out to provide a wider footprint and greatly improved traction in soft sand. You would commonly reduce the air pressure for your street running wheels from, say 35 or 32 psi, down to 12-15 psi in soft sand. Here's my Land-Cruiser in the soft Coral Pink Sand Dunes park in Utah. The ruts are fairly deep since I had not yet aired the tires down to 15 psi in soft sand.
But under a heavy load or on rough terrain, these low air pressure tires can separate from the underlying wheel itself to lose air pressure or go flat. Now the Trax wheels work great on soft sand and flat-surfaced roads/parking lots (with a normal load), whereas the standard older Hobie wheels will not ride up on soft sand beaches at all, and you are forced to drag your wheels (and loaded yak) thru the sand rather than up and over it, as you can do with the Trax wheels. Setting your tire back on the wheel (with no load on) and airing it back up slightly should reset the tire on the wheel and correct the "exploded" situation. Hope this helps.