"Is the cake sour?"
As an English-speaker, note that in the USA, a lemon may be described as tart or sour.
But, sour can also be used to describe a food that has a taste of being spoiled. Spoiled milk. Spoiled food equals rotting or rotten food.
Certain pickled foods have a lot of vinegar. We call pickled cucumbers "pickles". The ones with a lot of vinegar are described as sour or tart or tangy.
So are 시다 and 신 closer to the sour of lemons, but not the pickles made with lots of vinegar flavor?