In Arc GIS server there are many types of services are available (like feature service, Map Service, Geo-processing service etc.,). My question is in general web service whether it is ASP.NET web service or WCF service are like same or different with respect to map services in Arc GIS server.
These services are neither ASP.NET web services, nor WCF Services. It doesn't make sense to compare them to either, because they are very different from Both.
Till ArcGIS Server 10.0, there used to be a Java version & a .NET version. From a client's point of view, there was very little difference in these two.
You could also access the services using ArcObjects, DCom & the WebADF.
With ArcGIS 10.1, the service are totally separated from IIS and .NET and use something called the ArcGIS Web Adapter, that sits in between your webserver & ArcGIS Server.
All you can say is that the ArcGIS server's services can be accessed using the REST Endpoint, and the SOAP endpoint, over the HTTP protocol.