By starch, I'm assuming you mean glycogen, or animal starch. Similarities: Both are polysaccharide molecules made from glucose molecules linked together in a long chain. Both are storehouses of energy.
Differences: Glycogen is made in animal cells and is the only form of starch animals can digest (unless they have certain microbes in their intestinal tracts to break down cellulose, which all herbivores need). Cellulose is made in plant cells.
The bonds are a bit different; the molecules are isomers. Glycogen bonds with what is called an alpha 1,4 bond, meaning that the first carbon of one glucose molecule is bonded to the 4th carbon of the next glucose molecule, but in a way that puts the bonds in a shape that falls below the plane of the molecule, and allows branching.
Cellulose bonds with beta 1,4 bonds. The first and fourth carbons of adjoining glucose molecules are still connected, but the shape of the bond falls above the plane of the molecule and does not branch.
Since enzymes are specific to their substrates, the enzymes shaped to fit glycogen bonds do not fit on cellulose bonds, which is why animals cannot digest cellulose on their own. In herbivores, there are microbes in their digestive tracts which can produce enzymes to break these bonds so the glucose can be used. In carnivores and omnivores like humans, there is no enzyme to break down cellulose so it becomes 'roughage' in our diets. It passes through the digestive tract without being broken down.
