Frailing is a way of playing the banjo also known as clawhammer. To obtain a basic frailing strum on a banjo, hold the right hand with the tips of the fingers touching the palm:
The middle finger should be slighty extended from the other fingers and kept relatively stiff.
Hit a string with the middle fingernail, plucking it.
Optionally, pluck a string with the thumb.
Strum several strings with the middle fingernail.
Optionally, pluck a string (usually the 5th) with the thumb.
The forefinger can be used instead of the middle finger. It is not important which of the two fingers. What is important is that the fore or middle finger, whatever the case may be, be kept stiff. There should be no "flicking" motion with this finger.
The result is melodic but can have a strong strummed rhythm which allows the frailed banjo to stand well as a solo instrument. The dynamic range of the instrument is quite good when played in this way.
On the banjo, the most common definitions are that frailing means always picking the drone string, and clawhammer allows you to pick other strings with the thumb, which is also called "double-thumbing" or "drop-thumb".
In guitar, Steve Baughman, a skilled player and prominent proponent, defines "frailing" as using the index finger for picking melody (which is done by up-picking) and the middle finger for strumming, and "clawhammer" as using only downstrokes with one finger as is the usual technique on the banjo.
One usage of "clawhammer" in guitar circles refers to a style in which the pinky finger or the pinky and ring fingers are used to brace the hand and the index finger, middle finger, and thumb are used to pluck the strings.