Tear sheets are when your work is published in a magazine. You bring in the actual page from the magazine.
Call sheets are put out by production companies (mostly) and list everyone involved with the project & all the information you would need to know (title, phone #, call time).
They both prove that you are working professionally in the field & aren't just something you can make up just to get the discount. (The industry doesn't count weddings as "real" freelance work)