Is there any word for "small hand written note/letter" in English?

• a message
• a note, a short note

• message (noun) A usually short communication transmitted by words, signals, or other means from one person to another. TFD

• note (noun) "a brief informal letter" TFD

You could say "I'm sending her a note of appreciation".

missive

I've actually never used it before and my impression is I mostly hear it in clichéd phrases. Wiktionary considers it formal and defines it thus:

A written message; a letter, note or memo.

There is a commonly used phrase borrowed from French.

A Billet Doux is a hand written love note.

Frequently pronounced Billy Doo when used this way but often pronounced in the French way.