Two design choices, one you push the sides together so when folded it stays the same size front to back but flattened side to side. Second type folds sides in and get longer in the other axis top to bottom.
A third type perhaps the oldest design fold front to back and often allow for stacking used in church or school meetings. Last one is less comfortable IMHO having sat in them for many hours at meetings or fund raisers.
I like first two for comfort depending the the individual chair maker. Prefer the second that elongates getting smaller in two of three dimensions. Bought a nice one in Walmart for $20 and another in Sams. They fit in smaller spaces like a roof box over my car. One of mine has a shoulder strap for easy carrying and a locking piece that keeps it folded.
Have two adjustable lounge types very comfortable but much heavier and fold flat but still fairly large and heavy. Bought mine through mail order from Costco for $100 each. Think the French invented but we improved the design and made them for much less $$$.
