Can sleep password and screensaver password timeout settings be different?
No this isn't possible.

Nonetheless, this would be a great general security improvment for MacOS X.
For example since I type it pretty regularly but in a safe context, I would like to have an independant password to unlock my screensaver.

I suggest you to make your question a good proposal of security improvment
on the Apple feedback web server, section about MacOS X, since they didn't yet put in place a section about security feedback.