Check Billing and shipping info to be the same using Drupal commerce module?
No.

I recently added this feature to the commerce shopping module (both 1.x and 2.x branch). It hasn't been widely tested yet though, but I am using it for a production site and haven't seen any problems.

It's available for the 1.0 version or the 2.x-dev version.

This feature has been moved to Drupal Commerce in the 1.4 release (at the time of writing yet to be released), which means right now it's in Drupal commerce dev release and not in the 2.x-dev release.

The setting can be found under:
/admin/commerce/config/checkout/form/pane/customer_profile_billing