Can the parent and child budgets be created in different budget category?

If parent budget is created using one budget category (with approval rule1) and child created using another budget category (approval rule2), then two issues are noted.

1. child budget does not require approval (even though a different approval rule for this second budget category is setup)

2. parent budget amount is not getting distributed to child budget (Eg: parent budget amount =100, child budget amount=40, after child is created and becomes active, parent budget amount remains 100 and does not change to 60. If both the budgets are created using the same budget category, then as expected 40 out of the 100 from parent gets allocated to child and parent budget balance becomes 60)