This is mainly handled at a lower level than IIS - incoming requests are really just another tcp/ip sockets connection and as such these are identified by a unique IP / Port number combination.
Normally IIS wouldn't need to care - it gets a request, sends a response and forgets all about the request immediately afterwards.
If IIS is required to maintain information (state) about a client between requests then you would use some other mechanism (viewstate, sessions, querystrings etc) to programmatically control this.