Push Notifications on MacOS?

Hello everyone,

I'm a bit new to MacOS/OS X. I was just wondering if Mac apps to be open/launched/in the background to receive push notifications? I'm a long time iOS user and I thought push notifications would act the same on MacOS. On iOS the app you are receiving a push notification for does not need to be open in the background.

For instance, on Mac, I do not get a notification with Tweetbot when someone follows me unless the app is already open. Is this normal behavior? On iOS Tweetbot does not need to be open for me to get a notification. Yes, I have notifications on both in System Preferences and in Tweetbot's settings. I'm just using Tweetbot as an example. I don't get push notifications for Apple Mail app or one downloaded from the App Store either. I do however get Safari and iMessage notifications when they aren't open. Are there only a select few Apple apps that can do this?

If anyone needs any more clarification I'll be happy to provide as this is really bugging me. I thought it would function the same as iOS, correct me if I'm wrong. I'm on the latest OS 10.12.4