Is eye strain be caused by shortsightedness?

Usually not. There are muscles inside the eyes that contract when near work (like reading) is being performed. Prolonged periods of such contraction can lead to eye strain and headaches; glasses can support those muscles so they don't have to work as hard. Shortsightedness, or myopia, is inablility to focus at distance. Generally things up close are in focus.
Yes. Eye strain is a physical feeling. It is usually not accompanied by anatomic eye changes. "shortsightedness " which is uncorrected by glasses can give the person feelings of strain. Not wearing glasses will not damage the eyes in a permanent way.