Q:

Firefox Addons and chrome Extensions

What makes Firefox and Chrome and different in that Firefox needs restarting for most addons whereas Chrome does not? What are the differences between restartess addons and the other ones? 

A:

Depends on how the browser is build. In order to change/overwrite files they may need or not to be released (not in use).
By restarting the browser, the files are no longer in use and can be re-written.
It may also happen if a cache is needed and cannot be written while in use.
Quoting a Mozilla Dev, Mr. Dave Townsend:

I’ve just implemented support for a special kind of extension that can install (and uninstall, and enable, disable, upgrade and anything else you can think of) without the user needing to restart Firefox. This is of course to allow add-ons developed on the Jetpack platform to install without restarts but the feature is going to be available to any extension author, there are just some restrictions to how these extensions work.(...)

Quote source
When running Chrome, if you check your task manager you will notice several chrome.exe instances. Chrome uses several modules at once, therefore to reload the addons it wont need to restart totally. In Firefox's case, all you get as extra processes is the maintenance server for errors and the plugin-container process which allows flash content caching and processing among other features. 
Plugin-Container info
Several instances of Chrome.exe - explanation

