Dulce de membrillo and (Portuguese) mermelada are the same thing. In fact, in Gallego, dulce de membrillo is called marmelo, much closer to the portuguese word for it. In Catalunya it's "codonyat" (the quince itself is called codony in catalan, and codoña in some other parts of Spain).

I always thought that the English "marmalade" and the Spanish "mermelada" had a somewhat shared history, since in both cases, the portuguese meaning is lost and it picked up a similar meaning (jam type preserve). It's probably because the process of creating a jam is quite similar to that of creating a quince cheese, but with different fruits. Perhaps at some point, the word became a description of the technique, and not of the particular ingredients used.

just to complete the collection: in italian marmelade is "marmellata", while quince cheese is "cotognata" (quince being "mela cotogna").

The story here in Scotland is that "marmalade" was invented to make use of a consignment of bitter oranges:

https://en.wikipedia.org/wiki/Marmalade#Dundee_marmalade

My dad cooked dulce de membrillo every year :-)

When you're boiling quince with sugar you have to keep stirring the paste to stop bubbles from forming. Those damned bubbles burn bad in your hands, so when you start you cannot stop until it all done.

Maybe wear long oven mitts? I do that sometimes when frying foods.