Ask HN: Splitting Browsers for Privacy?

Networking question here:

(Note that I'm using "Google/Gmail" as an example, any other company name could be used instead).

Assume a typical home user setup, with a typical consumer router providing access to the outside world. A user logs into Gmail from one browser (Chrome), and then runs search queries from another browser (Firefox). Clearly cookies can't be used to track the search queries, since the browsers are seperate, but is there any other way google (or an equivalent service) could be tracking users under this scenario? Obviously both browsers will be sending data from the same IP address, but given that the outside IP address is using NAT, I'm guessing there's no way of telling from the outside that both data streams are coming from the same computer?