The Plantagenets | The Royal Family
If you want to see the full complexity, here is the family tree
https://www.britroyals.com/royaltree.asp
showing how Queen Elizabeth can trace her ancestry through most of the previous monarchs of Britain and England, to Alfred the Great.
The House of Tudor was started by Henry Tudor, who was the great-great-great-grandson of King Edward III on his mother's side. So, he's related to the Plantagenet kings of England.
After the Wars of the Roses between the House of Lancaster and the House of York, who both claimed to be legitimate heirs to the throne, Henry Tudor was the last man standing (so to speak). He was of the Lancasters; he married a daughter of the House of York, and stopped the wars that way. He then declared himself King Henry VII, of the House of Tudor. The symbol of the new house was the Tudor Rose, which combined the red rose of Lancaster with the white rose of York. And peace ruled over the land …ish.
The House of Windsor is actually the House of Hanover renamed. Twice.
When Queen Anne of the House of Stuart died in 1714, the British Parliament (which now had the power to choose the monarch) skipped over her 50 nearest relatives – all Catholics (because the British hated Catholics – long story) – to give the British throne to her far-distant Protestant cousin, Georg of Hanover, who became King George I of the House of Hanover. Georg was a great-grandson of King James I of England.
King George's great-great-great-granddaughter was Queen Victoria - still of the House of Hanover. However, she married a German prince of the House of Saxe-Coburg-Gotha, and thus became a Saxe-Coburg-Gotha herself, as did their children and grandchildren.
When Victoria's grandson, King George V of the House of Saxe-Coburg-Gotha, was on the British throne, his British subjects went to war with his German cousins in a little conflict known as the Great War. Deciding that discretion was the better part of keeping his head and throne valour, he changed the very German name of his house to something nice and British and safe: Windsor (after Windsor Castle).
So, yes, the House of Windsor is descended from the House of Tudor and the House of Plantagenet - through one of Henry VII's daughters, who married a Scottish king and whose great-grandson was King James I of England (at the same time that he was King James VI of Scotland), then through James' great-grandson Georg of Hanover (King George I), who is Queen Elizabeth II's great-great-great-great-great-great-great-grandfather. There are probably also other lines of descent over the centuries and generations, but these are the official ones through which the monarchy traces its claim to the throne.
https://www.reddit.com/r/AskHistorians/comments/17wzda/is_the_house_of_windsor_related_to_the_house_of/
moar on "houses" here:
https://www.reddit.com/r/AskHistorians/comments/16i7z3/comment/c7wcu6w/