In fact, there are various way Google is identifying the requests that are done, and most of the time the way it is done is related to your use case.
For general use and using the 'free' version:
You can track the usage by specifying an API key even if it's not necessary anymore.
The requests are managed by URL (referer) and by IP address.
For general use but with needs to buy additionnal quota:
For Business users:
You will need to include the key inside the script reference to the control, see: https://developers.google.com/maps/documentation/business/clientside#Accessing
Also, here is a summary view of what should be used depending on the type of service you're using as an Enterprise customers: https://developers.google.com/maps/faq#keysystem