What's the difference between APNs Distribution iOS and Apple Push Services?
The "Apple Development iOS Push Services" and "Apple Production iOS Push Services" are the old names for the certificate when you needed to have separate certificates for the two environments.
Now, you only need the one certificate for the new HTTP/2 API, so they've changed the name of the certificate to something more general - "Apple Push Services".
There's some good info on it here: https://matthiaswessendorf.wordpress.com/2015/06/17/wwdc-2015-apple-push-goes-http2-for-apns/
Apple's official documentation here: https://developer.apple.com/library/ios/documentation/NetworkingInternet/Conceptual/RemoteNotificationsPG/Chapters/ApplePushService.html
WWDC 2015 "What's New in Notifications" video here: https://developer.apple.com/videos/play/wwdc2015-720/
You therefore shouldn't now be able to create certificates for the two separate environments. One of the major benefits of this is that the certificate that works for "debug" builds of your app (mainly those installed directly onto the device via cable) will also work for builds that you send to your testers, and also for production builds.
Looks like now production certificates work in the development environment too (but not vice versa). So that's why Apple changed the name of the production certificate to something generic: Apple Push Services:...
Their is a big difference between “Apple Development iOS Push Services” and “Apple Production iOS Push Services” certificates . One is used for sandbox and the other is used for the production push server. Make sure you use the appropriate certificate for testing and production and do not confuse with those
The two kind of push SSL certificates as you have mention above i.e Development and Production. Development push SSL certificate will only work if you attach your iPhone with your mac and directly compile on your device. When you use Development Push SSL certificate Apple's demo server will be used to send notifications. Whereas when you create the app file or .ipa file and install that on device you need to use production push SSL certificate. You can not mix and match these certificate.
Hope it will clear your doubt... :)