When you open a Google file shared with you and select 'Add to My Drive', you are moving that file into your own Google Drive for easier access to the document. If your instructor or someone else owns the file, any changes they make to it will be updated in the file housed in your Google Drive. It is a living document that is updated in real time. If the owner of the document deletes the file from their Google Drive, the file will be deleted from your Google Drive.

When you 'Make a Copy' of a Google file, you are duplicating the original document and making your own copy that you can edit, share with others, etc. Any changes you make to your copy will not be reflected on the original document owned by someone else. In addition, any changes the owner makes to the original file will not be reflected in your copy.

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