Weigert's iron hematoxylin involves the use of ferric chloride as a mordant, which binds to tissue components and allows the hematoxylin to adhere more effectively. This results in a black or dark blue coloration of cell nuclei and elastic fibers. On the other hand, Weigert's resorcin-fuchsin uses a combination of resorcin and basic fuchsin to stain elastic fibers a deep purple or black color, making them stand out against a lighter background.