descendants of Princess Beatrice and prince Henry of Battenberg and those of her niece Victoria of Hesse and his brother prince Louis of Battenberg. Only the line of Louis and Victoria continues in the male line in the UK.
Descendants of princess Mary Adelaide of Cambridge and Duke Francis of Teck. Their oldest son prince Adolphus of Teck became the first marquess of Cambridge. Their second son prince Francis of Teck died before WWI and the third son prince Alexander became the first Earl of Athlone and was married to princess Alice of Albany, cousin of George V (Alexander's brother in law through Mary of Teck) and Alice was the sister of Carl Eduard Duke of Coburg.
Princess Marie Louise and Helena Victoria of Schleswig-Holstein-Sonderburg-Augustenburg were the daughters of princess Helena and prince Christian. In 1917 when George V changed his dynasty's name from Saxony-Coburg-Gotha to Windsor, Teck became Cambridge and Battenberg Mountbatten the princesses remained princesses but without any land or area they went from HH princess of Schleswig-Holstein to HH princess.
More distant relations like the Gleichens did not change their name.
As for the titles in the UK the highest noble title is Duke but their status in society was such that you needed to be very wealthy to live up to what was expected of a Duke so the title of marquess was chosen as it carried less of a financial burden.
Louis Battenberg became Marquess of Milford Haven (a sea port)
His nephew Marquess of Carisbrooke
Adolphus Teck Marquess of Cambridge and his younger brother only had one surviving son and a daughter so became Earl of Athlone.
As for their status, both the Battenbergs and Tecks were morganatic branches of reigning German dynasties. Battenberg of Hesse und by Rhine and Teck of Wurttemberg. Their status in Germany was that of neither meat or fish but in the UK Queen Victoria was more welcoming.
Victoria Eugenia, Alice and Louise of Battenberg all married into reigning dynasties but they were only acceptable Royal brides because of their maternal line. Their mothers Beatrice of the UK and Victoria of Hesse und by Rhine were full blown Royals and that made the girls suitable brides. The same applied to Mary of Teck. Her mother made her a great granddaughter of George III. The fact that she was a morganaut did not matter in the UK but that she was not a foreign bride with political links to another country than Great-Britain was seen as a positive attribute.