Hi,
Are you sure you're using HikaShop 5.0.2 on your Joomla 3 website ? Because the address_type field should be there if you have the 5.0.2. Otherwise, you would get many errors as this field is now mandatory.
Before adding address_type, an address could be both a billing and a shipping address. Each address has an address_id. And the order_billing_address_id and order_shipping_address_id columns of the hikashop_order point at the address_id of the selected address. So in an order, you know if an address is for the billing or the shipping based on these two columns.
The address_type is used for the selecting the addresses during the checkout. Before, an address would appear both as a billing and as a shipping address candidate. So when you created a new address, it would automatically appear as both a billing and a shipping address. With recent versions of HikaShop, you create either a billing address or a shipping address, and it appears only on the corresponding selector during the checkout. So you can now have different addresses for billing and for shipping linked to your user account.
Now, when you migrate the data, you don't have to be too mindful about all this. If the address_type is empty, HikaShop will display the address as both a billing address and a shipping address. And if the customer changes the address on the billing address selector, then HikaShop will automatically split it into two addresses, a shipping and a billing address.