Activities are things that “the project” can control. The boundary of a project being defined by the reach of its contracts (with staff, consultants, suppliers and sub-contractors)
Outputs are the activities of the project (if services), or their results (if goods), that people and organisations outside the project can use e.g workshops, publications, trainings, etc. Ask here: What is available to who, and in what form?
Purpose level changes (outcomes), are changes in those people or organisations who have used those goods or services. Normally the project would hope to influence these (and learn about how it can have influence) but it would not be expected to control events at this level
Goal level changes (outcomes), are longer term changes in those same people or organisations, or others they have subsequently interacted with.