Marmalade comes from the Portuguese marmelada (quince jam) and in turn from marmelo (quince) based on the Greek melimēlon from meli (honey) and mēlon (apple). How, I wonder, did the Portugese quinces turn (seemingly via melons and apples) into Seville oranges?
Marmite comes from the early 19th century. It is a French word from the Old French marmite (hypocritical - with reference to the hidden contents of the lidded pot) which in turn derives from marmotter (to mutter) and mite (cat).
Etymologically unrelated words. But now emphatically British products: British yeast in the case of Marmite. I have read somewhere that French chefs now use Marmite in cooking. Some members of our family pronounce it marmeet as though it were the French word.
I have never, on the other hand, heard of a French chef using marmalade in cooking. My mother once invented a recipe consisting of chicken thighs baked in marmalade.