What is the difference between
Location Manager was introduced in Android SDK and can be used as a feature of android.
Location Client is something that's part of Google Play SDK and is introduced in the recent Google IO 2013.
One can understand that since Location Client is the latest, it is more efficient in getting the location with minimal energy(battery drain) with greater accuracy.
Google Play Services Team has cleaned up their code and moved LocationClient functionality into GoogleApiClient.
Tutorial for the same is available in http://developer.android.com/training/location/retrieve-current.html
On following link you can find IO talk about this subject http://www.youtube.com/watch?v=Bte_GHuxUGc