Say you are receiving records from users and different intervals and you want to eventually store them in a different format on a database.
Streaming to me means you're "pushing" to the database according to some rule. For example, wait and accumulate 10 records to push. This could happen in 1 minute or in 10 hours. You know the size of the dataset (exactly 10 records). (You could also add some max time too and then you'd be combining batching with streaming)
Batching to me means you're pulling from the database. For example, you pull once every hour. In that hour, you get 0 records or 1000 records. You don't know the size and it's potentially infinite