I was tiring to build an app which uses google maps for showing places and Pace API for searching places. but it is not being possible to build the app with two different AP
Yes you can use the Same Key for Both Functionality.
Note : Make sure when you Create API Key You need to Enable both API Google Map and Google Places API.
From Google Console. Where you have Created your Project. That's It.
After that Both API will Work with Single API Key.
EDIT 1:
Create Project using this Link If you havn't Created your Project in Google Console.
Then after select created project from list of projects you have.
It will show you All the APIS List. From that Enable APIS which you need to use in your Project.
Then add your Generated API Key in Manifest Android. That's It.