If I crop an image to 18x13 but then print it 10x15, does it get distorted, or does the top/bottom just get chopped off? If the latter, who decides which bits get chopped away?
It will not get distorted - you will either have white space and the whole image shrunk to fit, or you will loose the top and bottom.
It depends completely how & who prints it - Most systems will probably fit to width and crop the top and bottom (IE centred Horizontally and vertically).
If you print it yourself, you make the choice.
Generally your best bet when printing a file is to resize it yourself to the size you want before hand. Otherwise, you are leaving it up to the discretion (possibly automated) of the printer. It may crop, it may add white space, in very, very rare cases, it may scale (though that is very unlikely unless it is a home printer and weird options are set.) Rarely will you actually get exactly what you want.
It is always wise to ensure that your images are cropped the way you want them for each aspect ratio you are printing and to ensure that you have sufficient PPI of data to make them look the way you want when printed. (Generally 150 PPI for being viewed from a distance or 300 PPI for viewing up close.)