Oh, I think I understand a bit better now!
Is the sharing module connected to the Publicize module?
No, the 2 modules are different.
Is it possible to just have the sharing buttons without the Publicize module?
Sure. You can choose which modules you want to enable by going to Jetpack > Settings in your dashboard. If you are not interested in the Publicize module, but want to add a Facebook Share button to your posts, you can deactivate the Publicize module and activate the Sharing module.
An official Facebook share button below the posts, just as the sharing module in Jetpack but without adding the “WordPress”-link in the shares.
The official Facebook Share button originally didn’t include that link, but we’ve changed that behaviour in this commit. After taking a look at the documentation provided by Facebook for that button, I believe we should be able to remove the App ID that adds that WordPress link, it doesn’t seem to be required.
I submitted a patch here, that would remove the link by default, and would also allow you to replace that link with your own if you wanted to. We’ll consider adding this in a future Jetpack release, but if you’d like you could apply the patch to your own copy of Jetpack today. The changes are detailed here:
https://github.com/Automattic/jetpack/pull/2590/files
I hope this helps.