What is the difference between `damsel’ and `spinster’?

A `damsel’ is a young, unmarried woman; the word is mostly used in literary contexts, and is considered rather old fashioned. A much more common word nowadays is `bachelorette’. By the way, the first syllable of `damsel’ is pronounced like the word `dam’, and the `s’ that follows is like the `z’ in `zoo’ and `zip’. The main stress is on the first syllable.
A `spinster’, unlike a damsel, is usually middle aged or old. She is someone who has never married and her chances of getting married are remote. A damsel is single for the time being; she may choose to marry later on.

 Source: ‘Know Your English’ ( The Hindu) – May 28, 2007