hello Graf Bretlach,
As other indicated, it is indeed the Old Style versus New Style, a source for much misunderstanding
Before 1700, the difference was 10 days. So, William of Orange sailed from Holland on 11 November 1688 [NS, as used on the continent], and landed at Torbay on 5 November [OS].
As to the battle of the Boyne, 1 July 1690 [OS], this became 12 July in the 18th century when the New Style was adopted and on that date those marches take place in NI. (A bit silly, as the correct date (New Style) would have been 11 July ... )
In the 18th century the difference was 11 days, have the dates of battles like Blenheim, and the death of king William different in English and, say, Dutch and French sources. In Russia the Old Style was used until the revolution, which is why the October Revolution was actually in November (or the other way around ...) and Russian Xmas is celebrated somewhere in January.