Kinktionary
More like guidelines and a lot less like definitions.
Anal Sex
The act of having penetrative or oral sex with an anus using a penis or phallic shaped object like a strap on, fingers or tongue. Oral sex with the anus is sometimes known as anilingus where as anal penetration using fingers is usually referred to as anal fingering.
Most people tend to use the term anal sex to refer to the penetration of the anus by another person using movements mostly associated with sexual intercourse but one could consider any form of stimulation and/or penetration activity with an anus part of the umbrella term of "anal sex".
The use of a penis or another phallic shape object to facilitate anal sex does not change the act, anal sex is enjoyed people of all genders and orientations. Where anal sex is predominantly between a male bottom and a female top using a strap on, it is usually considered pegging.
Since the lining of the anus is very tender and can tear easily, it is usually recommended to use lots of lube and to take things slowly when exploring anal penetration. Being careful with the width of your insertions (start small and let the person move themselves towards the insertion), using protective gloves and trimming your finger nails (or putting small cotton balls behind your nails inside your gloves) are also good steps to take.
Painal
A form of sadism play where the goal is to cause pain to the receiver as a result of anal sex. This is sometimes combined with humiliation or submission. Pain may be caused by the receiver tensing before penetration, a large phallic object being used for penetration without stretching up or the sex being very vigorous. It is commonly used as a category of porn but may also be enjoyed by some masochists. This is often considered risky play due to the risk of tearing the lining of the anus.