In fact ideas, beliefs, models all string together though on the surface they are different. Of course you can classify or relate and find so many striking difference but at bottom they are not different and your beliefs become your ideas and your ideas are likely to be your faiths and a particular faith holder is likely to be your role model. If you for instance study Marxism and this ideal becomes your idea and thought and later on you try to stick to this ideal and you will have a great faith in Marxism thought that was an idea.
There is no clear demarcations to segregate one from the other. They are interwoven though externally they run in different directions and at some point they may meet.