Use Service Bus (Messaging) - For messaging. It’s about one application telling one or more apps to DO SOMETHING or GIVE ME SOMETHING. Receiving is done via polling (long polling) and usually, a namespace is accessed within/by a single organization.
Use Event Grid (Eventing) - For eventing when the applications are saying SOMETHING HAS HAPPENED. The service is designed to allow communication between multiple parties and can span multiple organizations as published and/or subscribers.
The rule of thumb is:
If you can trust the subscribers to connect to the broker, great, use Azure Service Bus.
Otherwise, use Even Grid.
