The Milky way IS the galaxy. Since it is wide and thin (a bit like a spiral Danish pastry) our position in it (out on one of the spiral arms) means that it appears in the sky as a milky "smear" across the sky.
It is made of billions of stars and other celestial bodies.
If you live anywhere with urban light (especially street lights) you will be unable to see it, it is faint.
It is possible to confuse illuminated cloud with the milky way.