Upper Saxony
It was particularly to distinguish the lands from 'Lower Saxony', a concept which arose later in popular usage (though never enforced) as a term for the original Saxon lands in north and west Germany (where Low German dialects had spread), in what is now the state of Lower Saxony, as well as the adjacent Westphalian region, Holstein and the western part of today's Saxony-Anhalt north of the Harz range (Eastphalia).
Saxe-Lauenburg
The Duchy of Saxe-Lauenburg (, called "Niedersachsen" (Lower Saxony) between the 14th and 17th centuries), was a "reichsfrei" duchy that existed 1296–1803 and 1814–1876 in the extreme southeast region of what is now Schleswig-Holstein. Its territorial center was in the modern district of Herzogtum Lauenburg and originally its eponymous capital was Lauenburg upon Elbe, though in 1619 the capital moved to Ratzeburg.