drag and drop is controlled by your workflow associated with your issuetype. Given that, I suspect that you have different workflows associated with your issuetypes. Where you can drag and drop between columns the workflow supports those actions but for the others "bug and security" the workflow does not.
Assuming you are using a Classic (aka Company Managed Project) project then go to Project settings > Workflows and verify this (that you have multiple workflows). Inspect the one that is behaving the way you want and then compare to the other. Decide what you want to the workflows to look like and modify to meet your needs.
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