WebServices are a form of remoting, since you are effectively executing code else where or on the same machine outside of you AppDomain.
Remoting (InterProcess) on the same machine or over the network, is different in the sence that you Marshal your object between AppDomain/ platform boundries through transparent proxies and serialization. Remoting comes with its complexities and can easily become very complexe. WCF has made things much simpler to maintain. Performance wise, I haven't compared both approaches and would definitely be interested to see how both fare in an InterProcess context. Since WCF can communicate with binary bindings and is not limited to the HTTP Protocol.
WCF has made this much simpler using Pipes for InterProcess communication.
In the end WebServices used to communicate via port 80 (standard) HTTP and Remoting could communicate via predefined ports and channels using different serialization formatters.
They have now been upgraded by WCF which now provides methods for these types of communications.