I know that smart people tend to think the same and that naming collisions happen once in a while, but is this just a mere coincidence or is there more to the story?
Here is a description of Google Wave as per Wikipedia:
Google Wave is “a personal communication and collaboration tool” announced by Google at the Google I/O conference, on 27 May 2009. It is a web based service and computing platform designed to merge e-mail, instant messaging, wiki, and social networking. It has a strong collaborative and real-time focus supported by robust spelling/grammar checking, automated translation between 40 languages, and numerous other extensions. It is expected to be released later in 2009.
And here is a description of Adobe Wave as per Adobe web site (no Wikipedia description yet):
Displaying a desktop notification is as easy as sending an email. Adobe® Wave™ is an Adobe AIR application and Adobe hosted service that work together to enable desktop notifications. It helps publishers stay connected to your customers and lets users avoid the email clutter of dozens of newsletters and social network update messages. Adobe Wave is a single web service call that lets publishers reach users directly on their desktop: there’s no need to make them download a custom application or build it yourself.
Of course, once you get into it things get more obvious, but can you really tell the difference between the two without reading more about each technology and watching preview videos?