DOS commands allocate devices for it's output. STDOUT which is used generally for informational messages that record the programs progress and STDERROR which is used for errors. By using >> %log%, you redirected the STDOUT data stream to whatever device %log% defined; by using 2>> %error% you redirected the STDERROR data stream to whatever device %error% defined.
I am not aware of a third device, but DOS can be quirky, so you never know.
Hope this helps.