What are the differences between traditional and modern short stories?

It is very important not to generalize here, but very difficult not to in some ways. This is because some old-time short story writers had a lot of trouble getting recognition and appreciation for their work because they tried to break out of the traditional mould, to be pioneering with new styles and new ways of expressing themselves. This is particularly true of those writers on the cusp of the 20th century - such as James Joyce or even F. Scott Fitzgerald.

There was a tradition to have the short story like a little mini-novel with lots of scene-setting at the beginning, traditional rising action and then a flourish at the end, often with a little pathos or a moral. The story was descriptive ,had a plot and was easy to follow.Nowadays, many short story or flash fiction writers make their stories unintelligible, like puzzles ,with shock endings! Look at Anne Enright (The Portable Virgin)for a less extreme version of this.