All forms are considered active until they're archived but beyond that, they can be in multiple combinations of states:

An archived form is removed from view on all of your iPads. It's still there, but you just can't see it, or launch into it for form filling.

Forms can be archived and unarchived as many times as you like.

As the name implies, no version of this form has yet been published. It's probably a brand new form that you're currently editing.

A form with unpublished changes has been published sometime in the past. But, since its last publish, it's had additional saved changes.

You should be mindful that you need to publish your form, after making changes, in order to see them on your iPads.

A published form is the current version on all of your iPads.