'privately-ordered' originates from English, specifically from the adjective 'private' and the verb 'order'; 'private' ultimately comes from Latin 'privatus', where the root 'priv-' related to being 'separate' or 'withdrawn from public', and 'order' comes from Latin 'ordinare' (from 'ordo, ordinis'), where 'ordin-' meant 'row, rank, arrange'.

'privately-ordered' developed as a modern English compound: 'private' entered English via Old French 'privé' from Latin 'privatus', and 'order' entered via Old French 'ordener' from Latin 'ordinare'; in Middle and Modern English the words combined to form phrases like 'privately ordered' used both as a verb phrase and as an adjectival past participle.

Initially, 'private' meant 'not public / belonging to an individual' and 'order' meant 'to arrange or command'; over time 'order' acquired a commercial sense 'to request goods or services', so the compound came to mean 'requested in a private (non-public) capacity'.