There are quite a few differences. We use both inside our network and some features that we like for Citrix vs Terminal Server (remote desktop) are:
<li>Web access: Citrix provides the ability to access published desktops or applications through a web interface. Microsoft Terminal Services requires some add-on to provide this access.</li><li>Published applications: Citrix provides the ability to publish a single application to a user's desktop where it looks like a local installation yet the processes run on the remote Citrix server. Microsoft Terminal Services has only remote desktop capabilities.</li><li>Performance tuning: Citrix provides the ability to tune the user sessions with features like load balancing between presentation servers in a farm. There is also the ability to tune other network and user session parameters in a Citrix implementation that TS does not provide.</li>
A Microsoft-centric comparison can be found on the MCP magazine website.
Another comparison can be found here too.
The client consideration can be a major issue when considering whether to use MS TS or Citrix. A good Citrix reseller will help you determine the best fit for your environment and not push you into the expense of Citrix unless the situation warrants the features Citrix provides over TS.