Hi,
The batch management ticks in the different material master views are present because different departments/processes may utilize the same material differently in transactions.
Say you are purchasing a material, producing it and also selling it (sort of a manufacturer + dealer scenario). The vendors you buy from provide a batch number for the material they supply and you want to record these batches for defective goods from the vendor. However, somehow, you do not want to report the batch during sales and hence, it does not make sense to keep your produced stock in batches. In this case, you will tick batch management in only the purchasing view.
For serial number profile, this is constant for a material across all departments. Hence, its given in a general plant/ sloc 2 view.