A stain is a coloring agent. You can get stains in various colors, IE Walnut, Mahogany, Redwood, etc. Varnish is a clear coating without any color agent in it. Although by virtue of applying it to wood it brings out a 'warmer' look to the wood.

If you have real mahogany wood, you don't need to stain it. If you have a light color wood such as pine or bass, you could use a coloring stain to give it a faux look of another type of wood. You can still stain your mahogany wood with a mahogany stain, which will make it look darker and 'richer' but you should experiment on some scrap pieces first to see if you like th result.