People are often confused between Chat, In-App Messaging, Live Chat and Push Notifications and use it interchangeably.
In-App Messaging:
In-app messaging (also known as in-app communication) is the act of messaging, communicating with users through a software application, either on a mobile phone or tablet device or through software on a PC.
In-app messages can include images and text, and it is expected to gain more multimedia capabilities in the future. It often includes a call to action to take users to a certain destination within the app.
Marketers favor in-app messages over push notifications for contextual content.
Popular In-App Messaging solutions: Kommunicate, Intercom, NudgeSpot, Urbanairship, Moengage\

Live Chat:
If you are using push notification for marketing campaign then use it wisely.