WEBM is video the way browsers like it: open, royalty-free and built to stream. It was born in 2010, Google, out of its VP8 acquisition, and its real weak spot is life outside the browser: editors, TVs and Apple devices get picky.
WMV is a time capsule from the Windows XP years: tidy little files with dated manners. Windows Media Video, usually inside an ASF container; once the backbone of DRM movie rentals. That makes it the right destination when what you need is old Windows archives and PowerPoint decks that still insist on it.