This is a very good question. The words "jacket" and "coat" are often thrown around as having an interchangeable meaning - while there is, in fact, a key element that distinguishes one from the other. Using either term incorrectly is not a fatal mistake by any means, but for someone who takes an interest in clothing, it helps to understand the difference.
First, let's get the word "hoodie" out of the way. The commonly understood meaning of a hoodie is an unstructured, unlined garment that is worn over something else (i.e. you would wear a t-shirt underneath) - and, well, it has a hood. Basically, one of these...