Is ''blurt out'' synonymous to ''jump the gun''?

Because they both mean to say or do something quickly isn't it synonymous?


blurt out:

to utter with a sudden burst of strong feeling

jump the gun

to do something too soon, especially without thinking carefully about it:

Hence the two big differences:

  1. one can only SAY things while blurting out, while jumping the gun can be any action
  2. jumping the gun must be too soon, while blurting out can be at any time.

For instance, if someone was keeping a secret from another person for a bad reason, he could suddenly realize that this will cause a lot of problems and blurt the secret out, without jumping the gun -- indeed, while being vastly tardy in telling it.