I want to protect the wood with stain, but I do not want it to become a different color. Is it possible to find a stain that is the same color as the wood? If I were to find such a stain, would the wood still become a different color slightly because of all of the existing shades?
You don't need a 'stain' to protect wood. There are however plenty of clear finishes available, that cause minimal color changes.
Wood color only exists in cartoons. Every single species has different colored wood and some species have vast differences across the species. That is part of the reason for stains with names like 'red oak', golden oak, cherry, walnut, etc. Each is an attempt to stain one wood to look like another, (or make a whole piece look the same, ie. staining a cherry table cherry to make the color more even.)
For what its worth I think a "natural finish" usually ends up best. I think this is what you mean by not stain it a different colour. Natural stains tends to deepen the colour that is already in your wood. One good choice is natural oil: http://www.woodcraft.com/Product/813373/(H)-Watco-Natural-Gal.aspx?gclid=CL2K7LOgnMYCFcGRHwodG_sBvg
Its always a good idea to try your finish on a piece of scrap.