Is the Map Api Key and Google Places Api the same?

Look at this link at android developers https://developers.google.com/places/android-api/signup#release-cert

You need an Android API key, not a browser key. You can use the same API key for your Google Maps Android API v2 apps and your Google Places API for Android apps.

No, each service (Google Maps V2 API and Google Places API) have and will generate a different API Key. But you can't use/declare both keys in your manifest in the same time. When you are using Google Maps and Google Places just use the Google Places API key only (com.google.android.geo.API_KEY), and it will work for both.