The identifier in server logs is IP address, which is useless for distinguishing users. On the corporate side, NAT hides all the visits of many people behind a single IP. On the consumer side, ISPs change IP addresses all the time so a single person will show up as multiple IP addresses.

Note that I'm just talking about distinguishing people, not identifying or tracking. A basic question like "how many people came to my website today" is more accurately answered with client-side analytics than by analyzing web server logs.