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According to a source, the answer lies in the what these substrate binds into. Because they differ in what enzyme they will attach into any substrate is exclusive for that enzyme only. 
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Amylase is a digestive enzyme classified as saccharidase (an enzyme that breaks polysaccharides).

Α-Amylase breaks down α-glycosidic bonds (1-4) within the amylose and amylopectin chains. Amylose is converted to maltose and maltose molecules, while amylopectin yields maltose, glucose and dextrin molecules.

Lactase is an enzyme found in mammals and some bacteria. Its main function is to allow the dissociation of lactose into glucose and galactose, which allows the digestion of milk.

Lactase has two main functions:

* It hydrolyzes lactose, a sugar found mainly in dairy products, glucose and galactose, which can then be absorbed by the body.

* The other role is a phlorizin hydrolase activity which comprises hydrolyzing in phloretin and phlorizin glucose, a compound present in the bark of certain fruit trees which is used in the treatment of diabetes and hyperglycemia.

As you can see, these enzymes are specific to their substrate, amylase attacks amylose and amylopectin, and lactase attacks lactose and possibly phlorizin. Another difference that can be seen is that the amylase acts on polysaccharides while the lactase acts on disaccharides.