How do mod updates interact with existing saves/characters?

This is me not knowing how mods really work... Will an existing save or character that uses a mod be "locked" to the version it was created on, or will it update on the fly, or will it vary from mod to mod? tutuapp

 For example, I created a character using version 1.0.2 of the Bard class mod, and used it in a save game. Then I updated to 1.0.3. Will the character in the roster reflect the new version? How about the save game?