hi
the arcDesktop products contain the runtime engine, but just support add ins
for standalone applications u need the single runtime engine (which is not free)
i think this comes also with the server
- web adf is for creating web applications working with arcgis server
- arc objects is, as you stil said, just the library. It is used by all GIS products, server as well
- arc GIS server is the server solution in contract to arcDeskop as client solution, i did not worked with it yet, but i think there it will be the same as with arcdesktop, the addins and stand alone applications
if you now develop some programm using gis functions only from the server i think it will work. but if u want to make (just) some operations or the view within a web application without the server u will need the runtime engine installed
you always need the runtime engine, but for internal use, within arcdesktop or arcserver, the runtime engine comes with those esri products
