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I'll stir the pot a little bit more.

If you want to simply classify handguns as SA or DA, then from the simplest description, you get:

SA - Performs only one action (i.e. causing the firing pin to punch the primer within the cartridge). Another way to look at this is it is releasing the potential energy stored in the springs that make up the firing mechanism.
DA - Performs two actions, with a necessary one being the same action of a SA. The other action is one that applies energy to the spring within the firing mechanism (i.e. cocking the hammer or striker). IMO, true DA handguns have what is called a "restrike capability" - that is the ability to pull the trigger and have the firearm perform both actions repeatedly.

Obviously there are handguns that perform a combination of the above - those being DA/SA, DAO, Safe Action, and the like. To further complicate and distort the initial simplicity of this concept, many of them fall in between because they are not true DA or SA handguns.