Butterflies and moths are basically two versions of the same design. The butterflies adapted to drink the nectar of flowers during the day, and moths to cover the night shift, so yes they curl up and sleep.
Moths often have feather like antennae with no club at the end. When perched, their wings lay flat. Moths tend to have thick hairy bodies and more earth tone coloured wings. Moths are usually active at night and rest during the day in a preferred wooded habitat.
Moths have very long proboscis, or tongues, which they use to suck nectar or other fluids. These proboscis are very tightly coiled not in use, like a hosepipe. When in use, the proboscis are uncoiled to their full length and in some species, that length is remarkably long. The Hummingbird Moth has a tongue that is actually longer than its whole body. The Darwin's Hawk moth of Madagascar has a proboscis nearly 13 inches long, evolved, no doubt, to enable feeding on deep throated orchids which grow in that region.
Not all Moths have long tongues. In some, the proboscis is very short, an adaptation which enables easy and effective piercing of fruit.
In some, there is no feeding mechanism at all. There are adults of some species that do not take in any food. Their brief lives as an adult are spent reproducing and they are able to acquire all of the energy needed for this from the fat stored in the body by the caterpillar.
Camouflage is a great defence in avoiding detection by a hungry predator. Some moths look just like lichen, others look exactly like the bark of trees native to their habitat. It has even been noticed that in city areas where smoke pollution is strong, some moths have actually developed a darker colouration than the same species that live in less polluted areas.
Another effective form of camouflage is colouration which can confuse a predator into either striking at a none vital part of the moths body or into missing it all together. The lines and spots on these moths would make aiming in on it difficult, especially when it is moving.
Another form of defence is where the moth takes on the appearance of a larger/or more threatening creature. This amazing ability is called 'mimicry'. This form of defence ranges from caterpillars with tails that look like a large venomous snakes head, to moths and butterflies whose markings make them appear to be large birds.
Moths heat up their flight muscles by vibrating their wings, since they do not have the radiant energy of the sun (being nocturnal) at their disposal to serve that purpose. Moths navigate by two methods. They use the moon and stars when available and geomagnetic clues when light sources are obscured.