| Taxonomically, insects are divided into orders, families, then genera and species. Things may have changed since I went to school, but this is what I learned. (There are other classification systems of Lepidóptera but this is the easiest.)
Butterflies and moths both belong to the order Lepidóptera, a well recognized order of insects characterized by the scales on the wings which come off like dust when handled. The name Lepidóptera translates as scale winged.
Butterflies and skippers belong to the suborder Rhopalócera, the adults of which are characterized by clubbed or knobbed antennae, wings lack a frenulum (more later), are slender-bodied and are mostly day-fliers. Butterflies are often highly colorful. Butterflies will often pupate as a chrysalis, free from a cocoon.
Moths belong to the suborder Heterócera, the adults of which are characterized by antenna of various types, usually not clubbed, wings have a frenulum, are stout-bodied, and mostly night-flying. Moth antennae are variously filamentous or feathered. Moths are often non-descript. Moths will spin a cocoon to enclose their pupa if they are not otherwise pupating in a protected situation.
A frenulum is a structure found on the hind wings of moths that allow them to hold their wings together in flight. You might notice that butterflies, skippers, and moths hold their wings in different positions when at rest. Butterfiles will alternatively hold them flat and raised, most often raised; skippers hold them raised; and moths hold them flat. | 
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