Apostrophe is when an absent person, an abstract concept, or an important object is directly addressed.
Example:
With how sad steps, O moon, thou climbest the skies.
Busy old fool, unruly sun.
Main Entry: 1apos·tro·phe Pronunciation: &-'päs-tr&-(")fE Function: noun Etymology: Latin, from Greek apostrophE, literally, act of turning away, from apostrephein to turn away, from apo- + strephein to turn : the addressing of a usually absent person or a usually personified thing rhetorically- ap·os·troph·ic /"a-p&-'strä-fik/ adjective Nancy Noyes
AUTHORIAL INTRUSION: Discussions directed to the reader and constituting a substantial break in the narrative illusion of reality are termed authorial intrusions. While ordinary descriptions are notauthorial intrusions, substantial essays addressed to the reader are. http://www.unb.ca/extend/wss/1146demo/glossary.htm
The difference to me between "apostrophe" and "authorial instrusion" is that usually in apostrophe, the author is addressing some absent person or thing, not the actual reader, and the actual reader is the secondary audience. In other words, when the poet says, "O, come with me and be my love" I know he had someone other than me in mind when he wrote it. The apostrophe is to her. She's the primary audience. I'm the secondary audience. With "authorial intrusion," however, the author is very cognizant of the reader sitting there with book in hand, and the author breaks into (and away from) the text to address this reader directly. Lind Williams