Dependence among Fulfillment Statuses and Payment Statuses

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Hi there!

I'm about to move from Woocommerce to Shopify and I am trying to understand the fulfillment statuses and payment statuses in Shopify orders, are they dependent? To be more specific, can order with Payment Status Authorized have Fulfillment Status Fulfilled, or Payment Status Refunded and Fulfillment status Unfulfilled?

I am a bit hesitant about this, as I am not sure how it works with Shopify?