Which is correct:
Nothing is simple it seems. Thanks for the excellent responses by the way.
As engineers and technicians a more practical response is appropriate. In one of the two pictures the load will respond. If it is a resistor it will get hot. If it is a coil a magnetic field will be generated. If it is a bulb it will light. Forget the physicists and their arguments about current flow. When the plus on the battery is connected on the triangle end of the diode good stuff happens. When the plus on the battery is connected to the line end of the diode nothing much happens. Similar reasoning can be applied to transistors and other similar devices. The symbols we have chosen for our parts may not be pedantically right (from some point of view), but they are the ones that are extremely widely used. If you stick with them you will understand published circuits, and others will understand your written communications. Which most people think is a good thing.
When you graduate to AC circuits you won't have to change this understanding much. And when you are in university level courses on solid state physics you will have sufficient understanding to use either convention without worrying about it too much.