The difference is in the approach but at the end the "same" OpenStack will be installed I explain. Mirantis has packaged the installation of OpenStack in a custom ISO based image so you dont need to lose time in a huge configuration.

Mirantis developed Fuel which is a set of many components : Astute, nailgun, and so forth (please chech official documentation)

Mirantis allows to install OpenStack in a very easy and automative fashion. Of course the packages of nova, neutron, cinder are the same even if they are embedded in mirantis custom repo. I suggest you to try to install OpenStack manually dor learning purpose

I don't know any "community OpenStack". As far as I know, Mirantis uses just the plain OpenStack software from git.openstack.org without changes. The Mirantis distro packages some OpenStack projects, and adds Fuel, which allows you to configure your cloud and to deploy and manage the hosts that run it. But then, Fuel is also an OpenStack project.