Yes, it is the same Royal Family. Here you have the Family tree:
About her jewels, D. Catarina probably took many with her to England, as well as some important cities of India and Africa, at the time belonging to the Portuguese Empire. The Indian cities were the beginning of the British Empire in India. The Braganza Family was the most important and the richest in the Kingdom and the collection on jewels of D.Catarina’s (D.Luiza de Gusmão) mother was famous. However the family had to sell many jewels (including some crown jewels) to pay the war against Spain (they were not particularly happy with our independence and tried for years to recover Portugal). Because of that I do not know if the family had many jewels at the time of D.Catarina’s marriage. However, late in her life, already a widow, HM returned to Portugal. The Cities remained British possession but her jewels probably came with her because she had no children.
Cristina, do not forget that D.Catarina also introduced the use of china and cutlery. Previous the arrival of D.Catarina, English people (the elite) ate in plates of gold (or silver?), cooling the food very quickly.