Banner is the image that you put on your webpages, its some sort of an advertisement of your page to another or a product/services that you want to endorse. The standard size of a banner is 486x60 (measured in pixels). Banner comes from different sizes.

Header Banner is the image that you can see at the topmost of your website. It shows the title of your site and a lot more. The size of a header varies on the templates that you use. Please refer to own-free-websites' info about this.

Although banner can be made a header banner too but since the size of it is so small, when you view it as a header banner, the images were stretched to fill the gap of the whole width of the screen.