When downloading Commerce Kickstart (which is a Drupal Distribution) you can choose to download different things:
- commerce_kickstart-7.x-2.X-core : This contains the commerce_kickstart profile and the core of Drupal
- commerce_kickstart-7.x-2.X-no-core : This contains the commerce_kickstart profile without the core of Drupal. You'll have to put it into an existing Drupal site (under /profiles/).
- commerce_kickstart-7.x-2.X : This contains the commerce_kickstart profile without the core of Drupal and the required libraries. You shouldn't choose that one ;)
It only depends wether you need only the profile or if you want the full site (with Drupal).
The difference between zip and tar.gz is only a compression preference.