Bettas are very territorial fish! The fish in the picture is a male because of the vibrant colour and big fins. Female bettas have muted colouration and/or vertical stripes on them.
When you put 2 male bettas in a tank , they will fight for the space hence one will end up dead. They fight for space by flaring up their colourful fins and swimming into the other fish. Their gills also expand. It sometimes happens when a female is introduced to a tank with a male in it. I dont know why he attacks her
The best thing is to partition the tank if possible or seperate tanks but 2 males in a tank is a recipe for disaster.
Hope this helped.
Franco