LDO stands for low drop regulator. This takes a higher DC poorly regulated or regulated voltage and converts it to a lower regulated DC voltage. It is basically a special linear regulator that requires less voltage drop from the input to the output than a standard linear regulator.
A band gap reference is one type of voltage limiting device that provides an accurate reference voltage at a very low current. It is more stable than other devices such as a zener diode.
LDOs supply current at a relatively fixed voltage. You can see the output voltage tolerance and variation with load, temperature and from device in their data sheets. They are not intended to provide an accurate voltage reference.
bandgap references provide an accurate voltage at an extremely low currents. They are not intended to supply power.
