Packets are generally small and may contain food items like rice, but sometimes they sell small packets of daily vitamins. Bag are generally a lot bigger, like a shopping bag, which would be given when you went to the supermarket to purchase your groceries. Some people even use bag or bags when talking about their luggage.

In your context, yes. A packet is always closed, whereas a bag may be closed or open. When talking about shopping, I understand a bag of rice to be much bigger than a packet.