The first (larger) tree appears to be coast redwood (sequoia sempervirens), very different than the giant sequoia (sequoiadendron giganteum) in the second photo.
For the record, I have both as well. Obviously the coast redwood needs serious winter protection in my climate, but I've had one for about 5 years now. Hasn't been styled yet, just growing for trunk size. Needs major root work this spring...if spring ever gets here!
Chris