Android Market was renamed Google Play in 2012.
In 2013, the 2012 Google Play wordmark was replaced by the 2013 wordmark. This logo looks similar to the previous logo.
The previous wordmark was replaced by a new wordmark typed entirely in Product Sans, Google's current logo font shortly after Google introduced their current logo in September 2015. This logo was still seen on the Google Play store.
The logo was refreshed by giving the play button icon a flat look and saturated and brighter colors closer to Google's more recent color palette. The new icon was introduced on April 4th, 2016.
The type of Google Play badges (apps, books, etc.) have been combined into just one badge.