Saxons in Germany?

I understand that the Anglo-Saxons did not have a close connection to Saxony. The German Province of Saxony received its name after it was taken over by someone who had somehow been connected to a place called Saxony further to the north.

Here is a map and notes about the place called Saxony today:

Free State of Saxony
 Saxony
 https://en.wikipedia.org/wiki/Sa...
 From Wikipedia, the free encyclopedia
 Extract:

The Free State of Saxony[4] is a landlocked federal state of Germany, bordering the federal states of Brandenburg, Saxony Anhalt, Thuringia, and Bavaria, as well as the countries of Poland (Lower Silesian and Lubusz Voivodeships) and the Czech Republic…. Its capital is Dresden, and its largest city is Leipzig.

The area of the modern state of Saxony should not be confused with Old Saxony, the area inhabited by Saxons. Old Saxony corresponds approximately to the modern German states of Lower Saxony, Saxony-Anhalt and the Westphalian part of North Rhine-Westphalia.
 The Slavic and Germanic presence in the territory of today's Saxony is thought to have begun in the 1st century BC. 
Saxony-Wittenberg, in modern Saxony-Anhalt, became subject to the margravate of Meissen, ruled by the Wettin dynasty in 1423. This established a new and powerful state, occupying large portions of the present Free State of Saxony, Thuringia, Saxony-Anhalt and Bavaria (Coburg and its environs). Although the centre of this state was far to the southeast of the former Saxony, it came to be referred to as Upper Saxony and then simply Saxony, while the former Saxon territories were now known as Lower Saxony.

Here is a map concerning the Saxons of Anglo-Saxon association:
 Saxons
 https://en.wikipedia.org/wiki/Sa...
From Wikipedia, the free encyclopedia

The Saxons of north Germany therefore had little connection with the later Saxons of southeast Germany. Not only that but in the past it was remarked (by others) that the Saxons of Anglo-Saxon association in England may have been of different origin to the Saxons who remained behind or came into the former place of Anglo-Saxon habitat shortly after the Anglo-Saxons had left. 
 There were differences:
 The Saxons in Germany lived mainly further inward and were not seafarers.
 The Anglo-Saxons dwelt on the coast and were known as seafarers, sea-raiders, and pirates. Their habitat and language overlapped with that of the Frisians in the Netherlands. The Anglo-Saxons had hereditary kings whereas the German Saxons did not. The Saxons of Anglo-Saxon association identified with their allies, the Angles. The new land was therefore named Angle-land. The Anglo-Saxons were culturally closer to Scandinavians and included Danes and Swedes in their forces.