Casing shoes having drillable and non-drillable cutting elements in different regions and related methods

A casing bit, which may comprise a composite structure, for drilling a casing section into a subterranean formation, and which may include a portion configured to be drilled therethrough. Cutting elements and methods of use may be included. Adhesive, solder, electrically disbonding material, and braze affixation of a cutting element may be included. Differing abrasive material amount, characteristics, and size of cutting elements may be included. Telescoping casing sections and bits may be included. Embodiments may include: at least one gage section extending from the nose portion, at least one rotationally trailing groove formed in at least one of the plurality of blades, a movable blade, a leading face comprising superabrasive material, at least one of a drilling fluid nozzle and a sleeve, grooves for preferential failure, at least one rolling cone affixed to the nose portion, at least one sensor, discrete cutting element retention structures, and percussion inserts.