Not sure if you ever got this resolved... the difference that I think
you were missing is you can have different programs *running* in
different workplaces, but not different files/icons displayed on the
workspaces. The different running programs on each workspace allows
you to group your activities as you describe in your opening post.
There have traditionally been ways to launch certain programs in
certain workspaces, or you can switch to a given workspace and launch
a program in it. At least in Gnome 2.X (Ubuntu 11.04-classic and
below), the files (icons) displayed on all workspaces are tied to the
folder "Desktop" and there is no way to change that. Any
files/shortcuts saved onto one workspace will appear in all
workspaces. So you see the same icons on each desktop as the intended
behaviour. You can read some of the rationale for this on
launchpad.net (it's been a while ago, but I remember it was discussed.
It would take some digging to find it) I believe KDE offers
desktop-specific activities that can do what I think you are looking
for (i.e., have specific files and shortcuts displayed on different
workspaces). I have never liked the way they implement it, though.
Gnome 3.X and Unity also offer some different ways of grouping
launcher activities that you may enjoy reading about.