In the Moving an Issue documentation, its stated that issue type cannot be changed if the target project has the same issue type.

You may have set up custom issue statuses as part of a workflow. If you have assigned a custom status to your issue and it does not exist in your target project, you must select a new issue status for your issue. You cannot arbitrarily change the issue status, i.e. the option to change the issue status will only appear if you are required to change it.

However, sometimes it is necessary for the issue type to be changed.