For slotting use a router table, pushing a workpiece against a fence would probably be more accurate.
To follow a profile again a bearing guided cutter in a table may be easier.
To answer your question directly, a fixed depth router has the cutter exposed the whole time, a stand is needed to allow you to put the router down without leaving the cutting edge exposed i.e. standing up, small fixed base routers are good for repetitive work on something like a dovetail jig where you don't want the depth of cut to change or slip, small light work etc, but are a hassle if you have not made a stand for it.
A plunge router does just that plunges to a fixed depth, most bases have a three position stop to allow a gradual increase in depth of cut without excessive trouble, a great benefit if the eventual depth of cut is over say 5mm, you can set the depth stops to any depth, say 4mm, 8mm and 8.5mm to clean up the bottom of the slot.
And lets not forget you can buy a fixed base router with a plunge base as an accessory and if you fit the fixed base into a router table its easy to just slip the motor out of the fixed base/router table and put it into the plunge base for use outside the table, but would be an absolute pain to adjust for height whilst in the table.
The above is not an extensive list of the difference's, but will give you an idea.
Mike
EDIT: I have a couple of these:
http://www.supremeplumb.com/cgi-bin/DMd ... item=00078 I can't think the last time I used either of them in a plunge base, but I did buy them because of the low C of G to use on my Leigh dovetail jig, for which they are perfect, look around you can get them a lot cheaper.