Rather than using a custom field type, checklists in cloud are stored in an external cloud database, then rendered in the checklist UI on the Jira issues (read more about the difference between Checklists in on-prem and cloud). This page describes the different configuration settings, as well as differences in the UI.
In Checklist for Jira | Enterprise, some global settings can be overridden by project specific settings:
The UI on the issue panel is similar to Checklist for Jira, except that: