That's correct. Windows Messenger and Messenger Service are not related. But more than likely, it's the Messenger Service giving you those pop-ups. You dont have to take my word for it, take it straight from the horse's mouth:
<A HREF="http://support.microsoft.com/default.aspx?scid=kb;en-us;330904" target="_new">http://support.microsoft.com/default.aspx?scid=kb;en-us;330904</A>