Why does my order show "Manual Shipping" or a courier name next to Shipping?

The text after Shipping in the order's Summary is the shipping name saved with the order:

• When the order is placed, it's the label the customer saw at checkout, such as your Shipping Setup label or a zone method name. Manual Shipping is used when no label was sent.
• When you ship from the Fulfilment & Tracking box (pick a Carrier, enter the AWB / Tracking No., then Mark Shipped), it is replaced by the carrier saved there. That box needs a shipping carrier enabled for your store.

So a courier name means the parcel has been handed over through that box. The shipping amount itself doesn't change.