Both options are available.
In case you are looking to be only printing Amazon Logistics labels, use services called 'Amazon Logistics only'.
Is this printing all fedex,ups,usps labels using amazon account?
Linnworks requests eligible services from Amazon and the list of returned services/vendors can be seen by running Shipping Quotes in Linnworks.net (right-click the order > Action > Shipping > Get Quotes). Shipping label can be printed via Linnworks after accepting the suitable quote.
What is AMazon Logistics? Is it SOLE Amazon Shipping Service which they started? OR is it purchasing shipping thru amazon seller account (UPS FEDEX USPS)