Instead of connecting to another computer using Remote Desktop, can I somehow launch Windows Explorer (explorer.exe) and have it displayed locally but have it running on a remote machine?
Sure I can browse to remote machines using file sharing but if I want to move a file between shares it copies it across the network when instead it can performed instantly if I moved the file using the remote pc.
Hopefully that makes sense what I'm looking for...
Short answer: Nope.
If you're on Desktop A, and want to copy a file on Server B from \ServerB\Share1 to \ServerB\Share2, then the copy will have to go through the network to your machine and then back.
You can do this via RDP to ServerB, which you don't want.
You could do this through remote command-line as well, like telnet or psexec to ServerB. But that's not a GUI.
The only thing I've seen like this is WinSCP - if you use it to move or duplicate a file on a remote server that you've connected to via SFTP/SSH, it will do local commands to execute that. If you had an SSH2 server running on your ServerB, you could do it this way. WinSCP can be setup to look like Explorer.
I don't know if WinSCP will do the same via FTP, and it won't connect via SMB at all, and SMB doesn't have provisions for remotely performing a remote copy anyway.