The Differences Between Moths and Butterflies
Most species of moth are nocturnal (which means they are active at night), but there are crepuscular (active during the twilight) and diurnal (active during the daytime) species. Moths can be distinguished from butterflies in several ways. Butterflies are a natural monophyletic group, often given the sub-order ‘Rhopalocera’, which includes ‘Papilionoidea’ (true butterflies), ‘Hesperiidae’ (skippers) and ‘Hedylidae’ (butterfly moths). Moths belong to the sub-order ‘Heterocera’.
Here are some notable differences between Moths and Butterflies:
Moth Antennae and Butterfly Antennae
The most obvious difference is the antennae. Most butterflies have thin slender filamentous antennae which are club shaped at the end. Moths often have comb-like or feathery antennae, or filamentous and unclubbed. This distinction is the basis for the earliest taxonomic divisions in the family Lepidoptera – the Rhopalocera (‘clubbed horn’, the butterflies) and the Heterocera (‘varied horn’, the moths). 
There are, however, exceptions to this rule and a few moths (the family Castniidae) have clubbed antennae. Some butterflies, like Pseudopontia paradoxa from the forests of central Africa, lack the clubbed ends. The Hesperiids often have an angle to the tip of the antennae. None of the taxonomic schemes is perfect and taxonomists commonly argue over how to define the obvious differences between butterflies and moths.
Moth Wings and Butterfly Wings
Many moths have a frenulum which is a filament arising from the hindwing and coupling with barbs on the forewing. The frenulum can be observed only when a specimen is in your hand. Some moths have a lobe on the forewing called a ‘jugum’ that helps in coupling with the hindwing. Butterflies however lack these structures.
Most butterflies have brightly colored wings. Nocturnal moths on the other hand are usually plain brown, grey, white or black and often with obscuring patterns of zigzags or swirls which help camouflage them as they rest during the day. However many day-flying moths are brightly colored, particularly if they are toxic. A few butterflies are also plain-colored, like the Cabbage White butterfly.
Moth Pupae and Butterfly Pupae
Some moth caterpillars spin a cocoon made of silk. The caterpillars metamorphose into the pupae stage inside the cocoons. Most butterflies on the other hand form an exposed pupae which is also called a ‘chrysalis’ which hangs from twigs and tree bark.
However, there are many exceptions depending on species of moth or butterfly. For example, the Hawk moths form an exposed chrysalis which, however, is under the ground. Gypsy moths sometimes form butterfly-style pupae, hanging on twigs or tree bark, although usually they create flimsy cocoons out of silk strands and a few leaves, partially exposing the chrysalis. A few Skipper butterfly larvae also make cocoons in which they pupate, exposing a small amount of the pupae. The Parnassius butterfly larvae make a flimsy cocoon for pupation and they pupate near the ground surface between debris.
Moth Body Structure and Butterfly Body Structure
Moths tend to have stout and hairy or furry-looking bodies, while butterflies have slender and smoother abdomens. Moths have larger scales on their wings which makes them look more dense and fluffy. Butterflies on the other hand possess fine scales. This difference is possibly due to the need for moths to conserve heat during the cooler nights whereas butterflies are able to absorb solar radiation.
Moth Activity and Butterfly Activity
Most moths are nocturnal (sleeping during the daytime and being active at night) or crepuscular (primarily active during the twilight) while most butterflies are diurnal (active during the daytime and rests during the night). There are however exceptions, including the diurnal Gypsy moth and the spectacular ‘Uraniidae’ or ‘Sunset moths’.
Moth Resting Posture and Butterfly Resting Posture
Moths usually rest with their wings spread out to their sides. Butterflies frequently fold their wings above their backs when they are perched although they will occasionally ‘bask’ with their wings spread for short periods. However some butterflies, like the Skippers, may hold their wings either flat or folded or even in-between (the so-called ‘jet plane’ position) when perched. 
Most moths also occasionally fold their wings above their backs when they are in a certain spot (like when there is no room to fully spread their wings). A sometimes confusing family can be the ‘Geometridae’ (such as the Winter moth) because the adults often rest with their wings folded vertically. These moths have thin bodies and large wings like many butterflies but may be distinguished easily by structural differences in their antennae.
Generally speaking, those are the main visual differences between butterflies and moths, but you most remember that they are general rules and do not apply to all moths and butterflies. The similarities between the two are actually far greater.