Azure functions are small pieces of code that are hosted in Azure and they basically run after some trigger. Trigger could be a timer, could be a data change or a file that’s being stored, that trigger then calls some code to be run and causes some action to occur.
Event grid is also categorized as a serverless service, because it is actually doing a function. It is actually doing messaging, communication between the outside world, passing a message into Azure and then being forwarded on to a listener who is going to take an action off of that. But it is not programable in that sense. It’s configurable, not programable.
Logic Apps are a workflow service, if a workflow has multiple steps involved then that can be developed as a logic app. It operates on a if this then that principle, It can interact with both Azure and external services.