If you didn't know already, Google rebranded the Android Market to the Google Play Store. I personally didn't like the new rebrand, and many others agreed with me. However, it's here to stay and I'm sure Google have their own reasons for the new brand. I'm guessing they're onto something big.
If your Android phone hasn't updated the Android Market to the Google Play Store, you can download the APK right here and get the new version right away.