Fold-and-thrust belts are evidence of what we call 'thin-skinned' orogeny -- where most of the mountain-building is the result of folding and faulting of the uppermost rock layers (e.g. the sedimentary rocks overlying the continental basement rocks). You can think of it like taking a pizza and pushing all the cheese and toppings together without affecting the crust beneath. The Sevier orogeny of the western U.S. is a classic example of thin-skinned fold-and-thrust belt formation. Fold-and-thrust belts are now forming in front of the Andean and Himalayan mountains as well.
Alternatively, thick-skinned orogenies involve uplift of basement rocks (usually granite and gneiss) along deep, steeply-dipping fault zones (often the result of reactivation of pre-existing crustal-scale weaknesses). The Wind River range of Wyoming and the Uinta Mountains of Utah are both great examples of thick-skinned, basement-cored orogens that formed during the Laramide orogeny, NOT by a fold-and-thrust belt.
However, both thin- and thick-skinned mountain building can take place simultaneously. It is possible that the basement-cored uplifts are more related to increased crustal buoyancy resulting from flat-slab subduction, whereas fold-and-thrust belt formation is a more common result of compressional deformation of thick sequences of sedimentary rock above the basement.Hope that helps,