A subject is like a topic; it addresses what something is about. A subject is usually a noun phrase, and it is a simple fact. Examples - The subject of the book is a girl. - The subject of the movie is dinosaurs. - The subject of my paper is American history. A theme, on the other hand, is a concept or idea that could be described as the message of something. Or a word / phrase that connects everything in a paragraph, book, movie etc together. They address deeper issues that come from the subject. Examples - The subject of Jurassic Park is dinosaurs. The theme is to not mess with nature because it will end badly for you. - The subject of my paper is a Giant Panda. The theme of my paper is about how Giant Pandas are rare due to hunting.

Subject = what we talk about. Theme = how, in which way, we talk about it.