Multiple Checklists for Jira are available for all hosting options - Jira Cloud, Jira Server, and Jira Data Center. The feature set and the user interface on all of those options are the same, which means that you can freely migrate to another hosting without any loss of features or the need to onboard users with the app again.
Global templates are not automatically migrated and you are expected to migrate them by using our script to the new hosting. The process won’t take longer than 5 minutes. All templates are migrated with automation (configured with issue types or JQL).