I have created a workflow in which I need to have both an approve/reject task type and a type where the assignee must indicate they've processed the associated request. I have created custom task types based on the Workflow Task (SharePoint 2013) type, and associated these types with the workflow's task list, but cannot seem to find where I assign one over the other when creating the workflow in Designer. Any assistance would be appreciated.
When you create a task in the workflow in SPD, simply change the content type to match the one that you want for that particular task. For instance, in the 'Start a Task Process' dialog, expand the 'Outcome Options' section and change the 'Task content type' as required.
In the screenshot below, the highlighted portion is where you can select the appropriate custom content type that you've created.