They aren't, but share some similarities. OpenVZ can be considered an inspiration for LXC. (Which was mostly implemented by RedHat and not Google.)
Correction. The LXC project was mainly Daniel Lezcano and Serge Hallyn from IBM. Then some cgroup support from Google. And then Canonical hired Serge Hallyn and Stephane Graber to continue work on LXC around 2009 where they have continued to develop it till today. Docker based off LXC in 2013.