host name vs. device name vs. local domain name vs. gateway name

:-)

My router (a D-Link DIR-652) allows me to set a "host name" (on the internet
setup page), a "device name" and "local domain name" (on the network
settings page) and a "gateway name" (also referred to as "system name") (on
the administrator tools page). I'm a bit in the dark about the use of all
these names, and the manual isn't all that helpful.
So far I've discovered that I can go to the router's configuration interface
by entering the "device name" in a browser, instead of the router's IP.
Can anyone explain under what circumstance these names are useful/important?
(e.g. for setting up a home network to share files and printers between
computers)

Thanks in advance,

Marc.