Many differences:
Citrix is MUCH more secure, you can run all the traffic in 128 bit SSL. You would need to setup a few boxes though, Citrix secure gateway, a ticket authority, a citrix server, and if you want to publish your apps on the web you have an NFUSE server.
Citrix is much more stable as far as how many users you can get running per server.
You have the ability to publish a single application to a user so if I am Joe I login and get Internet explorer, but John might login and have Internet explorer and WORD. You can do this using the Citrix NFuse page which is just a web page and the users will see applications or you can do this just using the server and ciitrix clients. You also have to keep in mind licensing which is big. Terminal server cals are around 80 bucks a piece for each client. Citrix requires that you use a terminal server cal and a citrix cal and the citrix cals are around 200 (I think) been a while since I bought some.
with citrix if you get alot of users you can take a couple servers and load balance the applications so each user will get moved to the server with the most resources available, fewest users, etc all depending on what you setup.
You can also run dumb terminals in the office and people can run an entire desktop on one using just the citrix server.
CItrix runs on the ICA traffic protocol and Terminal Services runs on the RDP Protocol. ICA Is much quicker if you compare the users experience.
Plenty more but most companies that rollout remote thin clients use citrix and as all MS products TS has alot more vulnerabilities.

- citrix clients for different platforms linux dos(very fast to boot from) Mac , windows
- Loadbalancing : when one server is down the other servers take the other client, this is not possible in Ts unless you define another server in the clientPC
- Shadow mode ( as admin you can get the screen of the user)
- you can run apps in seamless window : the user have the idea the the software is running locally.
- a very fast prtocol can be user over a very slow connection
- security is much better

the other side of citrix is
- expensive
- we had troubles with a client that took to much CAL's

Citrix is loading each program once to determine how much memory is used it then cascade these Sessions to get maximal benefit on the memory. The next Session will just be a window but not the whole program.

TS for each Program that is opened a new Session is made and that's why you will see that when using the Citrix program much lesser memory is required and they run more stable using the Citrix.