Is it not possible to create a separate exalate button but there are different ways you could achieve this:
Option 1:
Having separate connections, one dedicated to Change Request and one related to Catalog Task. You can trigger the sync from the exalate button, selecting the right connection. Also you can trigger the sync using workflow post functions (these could be transitions that go to it self)
Option 2:
You could do the same with a single connection. On the Servicenow side, you could decide if creating the change request/catalog task based on any Jira field that is set on the replica, like a label, a component or a custom field.
One of my use cases is to have manual buttons in Jira to create different things on the ServiceNow side. This would be instead of using an automatic trigger.
Is it possible to have 2 different Exalate buttons to do this?