There are differences between the encrypted Google search at https://encrypted.google.com and the ordinary HTTPS Google search at https://google.com:
Originally, the regular Google.com and http://www.Google.com usage was without HTTPS, and encrypted.Google.com was using HTTPS.
Even after HTTPS support was added to all Google subdomains there is still a difference in the referer handling: encrypted.Google.com is much safer.
–jeroen
The Wiert Corner - irregular stream of stuff 