The 1981has what looks like a mint over and the 1989 had a weak mint mark, multiple did cracks on obverse and reverse one can be seen by eye under mint on rim. The fg are completely different on the coins and both have doubling. almost everything on reverse of the 89 is doubled, the ribbons are also different sizes
I don't know much about those shiny metal discs, but maybe if you post this on a COIN forum you can get more coin aficionado's to take a look and chime in.
"Does anyone know why these two half dollars are different sizes?" I dent had them ost lest idea. Chris
Once again, let me remind you that you have posted this on the PAPER Money area of Coin Talk. Try asking the COIN collectors on a COIN thread.