thank you for your good questions!
I am sorry that I have little knowledge of designs.
what the difference is between logo and banner?

I regarded them as the same thing.
what I want is some design that we can put on the header area of our main page and fits our website. i hope that people will know easily what business we are doing and keep our name in mind without difficulty because the wonderful logo or banner.
Does it make
sense?
A logo and a banner are two extremely different things. A logo is a symbol, emblem, or icon (which sometimes includes the name of the company/product, usually in a unique font) which is designed to "brand" products and act in a similar way that a flag would for a ship at sea.
A banner on the other hand, is an advertisement or page-header that is more complex and can contain much more information then a logo. A banner can, and usually does, include a logo.
Let me provide you with an example. At Totally Wicked's website (
Electric Cigarette & E Liquid - Totally Wicked Electronic Cigarette Fluid), this banner serves as a page header, and it prominently features their logo in the center (the devil face smoking an e-cig):
However, their logo itself is only the devil-face, it is not the entire image above. A logo is something designed to be fairly simple and recognizable. I hope I've done a decent job of explaining this, but something tells me that the beers which I've consumed tonight will interfere with the lesson I was trying to convey.
Now that I know you are looking for a banner though, what size should it be?