Cellulose and amylose are both important organic molecules produced by plants, but cellulose is mainly used to serve a structural role. Amylose is used to store sugar that is produced via photosynthesis.
Cellulose is the principle component of a distinctive feature of plant cells, the cell wall. Cell walls keep plant cells stiff and allow a plant to grow tall and have access to sunlight even in crowded conditions like a forest floor. Cellulose bound in another organic molecule called ligin is what makes wood from trees so strong.
Amylose is a principle component of starch. It makes up about 30 percent of starch by weight. It has an extended molecular structure that tends to bind water, making it excellent for forming gels. The other component of starch, amylopectin, is also absorbent, but when it absorbs water it tends to swell rather than thicken the solution. Both molecules are used to store sugar inside plant vacuoles for when sunlight is not as readily available.
Both cellulose and amylose are complex carbohydrates. In cellulose, the carbohydrate chains are arranged in a criss-cross mesh of long molecules like beams inside a steel building. Amylose forms long unbranched chains that tend to twist into stiff helixes. Both molecules can be used as food sources, but humans lack the proper enzymes to break down cellulose. Other animals, including termites, are able to consume the cellulose carbohydrate.