Daisyl: The brown things are the berries which have dried (into seeds?).
AlyssaBlue: Yeah, that confused me that several different things seem to be called Thuja Occidentalis. The white cedar does resemble it, but it grows so tall, I don't think it's exactly the same. Mine is only about 5 feet tall and isn't getting any taller in 6 years. I just saw a photo of Eastern Red Cedar that seems to resemble it too.