Here is info on the Malicious software removal tool:
http://www.microsoft.com/security/pc-security/malware-removal.aspx. This explains a bit of the difference and why you would want MSRT and why you still need MSE even if you have MSRT. You cannot use MSRT in place of MSE - you will not be adequately protected
as MSRT doesn't provide real-time protection and is not as complete among other reasons.
Yes, it can be installed on your system at the same time as MSE - and I would actually recommend it. I have both installed myself.
MSE detects viruses and malware and spyware. MSRT detects and removes certain types of malicious software that may or may not be addressed specifically by MSE (or perhaps that MSE can detect but not remove). Still MSE is much more comprehensive and complete.
MSRT is supplemental security and it will not hurt to have both installed (though if you do scheduled scans with each (and you probably wouldn't officially set any up with MSRT and just let it do its own thing assuming Windows Update is set on automatic updates),
make sure they are for different times as running both simultaneously would probably not be wise and would be a severe drain on resources).