Input Method / Keyboard: Those are completely different things. An input
method is something like Anthy for Japanese input: using a small number of
keys to produce a lot of different characters (think thousands).
Onboard / Onboard Settings: As the name implies, "Onboard Settings" controls
the settings of "onboard" (the on-screen keyboard). "Onboard" just starts up
the on-screen keyboard.
Network / Network: I don't have this duplication, so it must be something
extra you installed.
Online Accounts / Online Accounts: Same, I've only got one of these.
Printers / Printers: I do have this. It seems Trisquel ships with a separate
program for configuring printers that it uses by default
(system-config-printer, some utility from Red Hat), but GNOME also has its
own printer configuration utility.
Software Updater / Software & Updates: These are completely different and
complementary. The former is a graphical utility for updating your software.
The latter is for configuring your software sources (it was called "Software
Sources" in Trisquel 6).
User Accounts / Users & Groups: I have this, and I'm not quite sure what the
story is. "User Accounts" is the one in the system settings dialog, but Users
& Groups has a lot more configuration options. It looks like "User Accounts"
is probably the official GNOME one, and "Users & Groups" is the one chosen
for Trisquel.