Wire does not use Signal Protocol. They used some of our code, but created a protocol of their own devising that we do not recommend.
We renamed the Axolotl ratchet and Axolotl protocol because there was a lot of confusion around what it meant to say "Axolotl." Some people who continue to use the term "Axolotl" do so because they seek to benefit from that confusion.
It is great that Wire has finally open sourced their software. They have been advertising themselves as open source for the past two years, though, so I guess they weren't really able to make an announcement about this.