There is no difference as such. I believe it's just a synonym.
The meaning remains same, "the subsequent requests are sent to the same app server which has created the session for the first request". This is achieved through a clone id in WebSphere Context. Meaning, every server in an app server cluster associates a clone id with session id. A similar analogy is being followed by other app servers like Tomcat, JBoss and Weblogic.
Further, the terminology belongs to an app server implementation context. Ex; JBoss and Tomcat uses "Sticky session" to explain same analogy where in webshpere uses "Session Affinity". That's only difference I see.
Thanks,
Krish