Right now it appears that your device is set up so that the adb shell is not by default root, and you have to use su to get a root shell. The DDMS file explorer in eclipse would not do so, so it would only have root access if adbd is set to run as root and provide root access to clients by default.
You could check this out from an adb shell with
ps
(and see if the 'ps' process is running as root or shell) or
getprop ro.secure
Using an su root shell, you could remount the root filesystem and change ro.secure to 0 in default.prop - amongst other things, this would result in adbd running as root and by default granting root shells. However, this has security implications and you may not want to leave it that way. You would need to do a web search for the exact shell remount command for your particular device (since the adb convenience one wouldn't work in the case where adbd was not yet root).
You could also see if the 'adb root' command would work to put the adbd into root mode.
It may be that your system is not 'rooted' in the sense of having any configuration changes made, but instead only in the sense that there's a custom su binary present which will allow unprivileged users who know about the possibility to get a root shell - the stock tools wouldn't know about that possibility and so would not be able.
