Facebook Like
Jetpack does indeed use the official Share button instead of the Like Button. This way the Facebook button behaves like the other sharing buttons, and actually shares the post instead of just “Liking” it.
If you’d rather have a Like button, you can install this small plugin I created, that will add the additional Facebook button as an option under Settings > Sharing:
https://github.com/jeherve/like-share-facebook-jetpack/archive/master.zip
You can follow the same process for Google+. I didn’t create any plugin for Google+, but you can build your own, starting from the other plugin; its code is available here:
https://github.com/jeherve/like-share-facebook-jetpack