Suppose I have an application in which people suscribes to receive a notification when some event in a bar is created. I would also like to draw an icon in a google map when a bar is added. I read about Google Cloud Messaging and also Firebase which Google advertises as the improved version of the former. What are the advantages and disadvantages of both?
Yes No Difference as you read, Google Cloud Messaging is the traditional way to send push notifications and downstream message to Android.
Now with the addtional of new product Firebase (bought), google making some changes for efficient use. So they just renamed GCM as FCM (new improved version), along the change now you using FCM can send push notifications to iOS devices as well and more new features,
In fact you can register push token using Firebase and send api signal to GCM server, still the message would reach the device.
You can read this FAQ, https://firebase.google.com/support/faq/#gcm-fcm