Question: As far as I can see a cape and a hood are mostly identical type of clothing. Does that mean that they are synonyms? What's the difference between them?

I was watching the cartoon and the movie and she isn't wearing a hood, she wears a cape and a hat there. Why is her name Red Riding Hood, what does riding mean? And why is her clothing called a hood?

P.s. Why *red riding hood* while it should be *red hat*.

Answer: 
Capes and hoods are not identical. They can be worn together, but they are separate pieces of clothing. Capes are sleeveless cloaks, often associated with superhero attire. Long, flowing pieces of material affixed to the neck/shoulder area in some fashion.

[![superhero cape](https://i.stack.imgur.com/MUFOom.jpg)](https://i.stack.imgur.com/MUFOo.jpg)

Hoods are a form of headwear, that cover the head and neck and expose the face. They often form part of a coat or cloak, and inspire the name *hoodie* for hooded sweatshirts and jackets.

[![man in hood](https://i.stack.imgur.com/FU1tVm.jpg)](https://i.stack.imgur.com/FU1tV.jpg)

As you can see, these are very different pieces of clothing.

With regards to your postscript, this is because hats and hoods are different classes of headwear. Hats generally do not cover the neck and have brims, which hoods do not have.
A riding hood is [*an enveloping hood or hooded cloak worn for riding and as an outdoor wrap by women and children.* - M-W](https://www.merriam-webster.com/dictionary/riding%20hood) This kind of garb was probably more common when people routinely got around on horseback (like in the days when popular old children's stories were written). Pulling the hood back off the head would make it blend in with the rest of the cloak. 

But in re-envisioning old stories into modern picture books or cartoons, original meaning is often lost. "Little Red Riding Hood" becomes the girl's name instead of a nickname based on a reference to her red cloak, and her outfit might be revised to be more modern and familiar to what children relate to. Similarly, "Goldilocks" becomes the girl's literal name instead of a reference to her hair color (if the story had been written today, she might have been called "Blondie").