They both use the same virus signatures and essentially the same scanning engine. So they should detect the same infected file, this does depend on the type of file, the scanner used, its sensitivity and its settings.
The standard shield and other shields are resident, on-access scans, they scan files before they are executed or downloaded, etc. to protect your system, the Web Shield and internet Mail providers (shields) scan content before it gets on to your system, if something is detected it can be dealt with before it gets on your system.
On-demand scans are initiated by the user and can be set to scan all of your hard disks or certain folders or files, you can also adjust the sensitivity and if it scans archive files, not normally scanned by the standard shield as they aren't an immediate risk, they need to be extracted and then run.
I suggest a browse of the avast help file.