All the series of Blackadder are related in the sense that the main character is meant to be a descendent of the previous Blackadder, but in each case several generations apart - they are not the same person.  Each generation is hundreds of years apart:

 - Blackadder is set in the Middle Ages.  The Prince Edmund character lives 1461–1498.
 - Blackadder II is set in the Elizabethan age.  Elizabeth lived 1533 - 1603 and she is young woman in the series, so we are looking at 1550-1570 period.
 - Blackadder III is set in the English regency period.  George ruled as Prince Regent from 1811-1820.
 - Blackadder Goes Forth is set in the First World War on the Western Front in 1914-1918

The character differences are most striking between season 1 and 2, as the writers changed and the budget was reduced, forcing less on-location shooting and a more on-set situation comedy approach, which IMHO dramatically improves the series. The last 3 seasons were all developed by the same team, and Blackadder is substantially the same character in the different eras.