Yes, yes, Cortana includes some rather excellent music recognition (hint: tap the music note in the Cortana home pane), but that doesn't mean that third party applications can't exist. Witness the cross platform Shazam, which has had several recent updates, culminating in the latest today, v126.96.36.199. Here's a summary of what's new.
Since we covered v4.0.0 here, there have been the following changes to the current Shazam v188.8.131.52:
Updated to a new version of Youtube to make the video pages even better
Preview your favorite Shazams with Xbox Music Playback
Get recommended songs based on your Shazams
Enjoy Xbox Music in Charts and My Shazam with more to choose from
Add your favorite songs from Charts to My Shazam
Trending Shazams: what's popular right now
Genre Charts: hip-hop, pop, dance, country
Future Hits: the 10 tracks you should know
Global/Local Charts: top 100 most Shazamed tracks worldwide and near you
New Lyrics and Video pages so you can stay connected to your discovered music
Installation on SD card enabled
As usual, I've done some screenshots for you:
Getting started, tap to start listening, etc.; (right) anything you've had recognised (rightly or wrongly) gets added to 'My Shazam', though you can long press to delete anything which you didn't want, etc.
A comprehensive rundown after recognition, with buy link, lyrics, videos (from YouTube) and recommendations - these are a little obvious, but hey....
You can tap through to buy tracks on Xbox Music (usually) and now there's a 30 second preview, perhaps to double check that it's the track you wanted.
Lyrics are looked up and presented well, with blurred cover art behind; (right) the 'Charts' pane acts as a discovery hub, showing what others have looked for, sorted by various locales and metrics....
Tapping through to videos produces content from YouTube, though there's no control over quality and other factors, so the experience here isn't perfect.
Recommended overall, though, for anyone wanting a little more in terms of music recognition - here's the Store entry (ignore the AAWP page, which may seem out of date - the links and QR code will still work fine). Note there's also the paid Shazam Encore, much the same but without ads.
Mind you, for casual users, and where Cortana is available, just use that instead.