Braces are simply handles on the teeth.  Braces are put on the front surfaces of the teeth with a special adhesive.  Braces can be metal or ceramic (clear.)  After all the braces are applied to the teeth, a wire is inserted into the braces to straighten the teeth.
 
Invisalign is a series of clear plastic aligners that straighten the teeth.  These aligners can be removed when eating and brushing your teeth.