Revolvers: Single action means you have to cock the hammer before you can fire the revolver by pulling the trigger.
Double Action gives you the option of (1) cocking the hammer back before firing the revolver by pulling the trigger or (2) firing the revolver by pulling the trigger all the way to the rear so it cocks the hammer back and releases it by it's own design thereby firing the revolver.
Double action only means only firing the revolver by pulling the trigger back all the way to the rear so it cocks the hammer (usually an internal, not exposed or external hammer) and then releases it by its own design thereby firing the weapon.
Single action semi-auto means cocking the hammer back for the first shot and pulling the trigger, releasing the hammer thereby firing the weapon and the cycling of the action automatically cocks the hammer back for following shots.
Double action only semi-autos function in a manner similar to double action only revolvers, in that although the cycling of the action ejects the spent cartridge and then chambers a fresh cartridge, the hammer does not cock back as it does with a single action only semi-auto but returns to a 'safe' position in which the weapon can only be fired by pulling the trigger all the way to the rear as with the first shot.
Hope this helps. Mikey.