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(Not) Activity was Logged triggers only on "Tasks" and "Events" that exist in Salesforce. Anything else that shows up in the SFDC Lead/Contact's activity history is not seen by that filter, unless it is also a task or event in Salesforce.
"(Not) Activity was Updated" will trigger when an attribute of a task or event is changed in Salesforce. For example: If you change the status of a task from "Not Started" to "In Progress" this will be seen by the "Updated" filter, but the creation or assignment of a new task will not.