They are related to some extent. The big differences were that Wave was built on XMPP, driven largely by and for Google, and put higher emphasis on collaborati

They are related to some extent. The big differences were that Wave was built on XMPP, driven largely by and for Google, and put higher emphasis on collaborative editing and threading and less on bridging. Matrix is non-profit opensource and focuses on defragmentation and bridging from the outset. Matrix also provides many more clients than were ever available for the Wave protocol, some of which have subjectively better UX. If Wave had bridged with protocols like email or IM, provided a clearer UX for newbies, and nurtured an open community and network rather than focusing primarily on Google's use cases, Matrix probably wouldn't be needed today.