Buddhist nun
Specifically a female Buddhist monastic; the term is neutral and commonly used in news and general writing.
About ten Buddhist nuns live at that temple.
Catholic nun; sister
Used for Christian nuns, especially in Catholic contexts. シスター is also common in everyday speech.
The nuns offer prayers in the chapel every morning.
She became a nun at a young age.
She spent her whole life as a nun.
シスター is the common, casual loanword for a Christian nun, while 尼僧 is a more formal, written term used in the same sense.
修道女 is the formal Japanese term for a Christian nun, roughly equivalent to 尼僧 in its Catholic sense, while シスター is more casual.
尼僧 is a more formal, written term for a nun (Buddhist or Christian), while 尼 is the shorter, everyday word.
尼僧 shares the 僧 character with 僧侶 but specifically means a Buddhist nun, not a monk in general.
counter for people
nunnery; convent
尼 (nun) + 僧 (monk/priest). The kanji 尼 originally referred to a Buddhist nun, and 僧 is a general term for a member of the clergy. Together they specify a female monastic.