The Museum of HP Calculators (
http://www.hpmuseum.org) has information
about both of these, and there have been discussions about repairs on the
forum there. The card reader is probably magnetic, but there appears to
have been an optical card reader available as an option, too.
The built-in card reader is certainly magnetic.
There were many periphjeral available for these machines, including a
mark-sense card reader (you know, fill in a Hollerith card with a
pencil), which I think was optical. AFAIK to do much with such
peripherls, you need the Peripheral Control ROM (PC-II is much more
useful than PC-I), which are very hard to find.
In case it's not obvious, the 'Model 10' ROMs work in a 9810, the 'Model
20' ROMS work in a 9820. The ROM modules are electrically identical, but
of course the ROM programming is very different.
-tony