Q: What is the difference between "Send Immediately" and "Send Automatically" with auto text messages an emails?
A: "Immediately" and "Automatically" are very different - the differences is this...
Immediately - sends the messages as soon as the activity is created (as soon as the workflow is started). This is normally reserved for the first email/text in a workflow.
Automatically - sends the message automatically based on the assigned date/time of the activity.
Both require that you NOT use checklists, repeating activities or Multiple actions. These are basic activities which should not take a user's interaction to process. If you do have checklists, multiple actions or it's a recurring activity, then automatic will not work "automatically". You will have to complete the activity and run the action manually.