Level-shifters don't store any energy. This means they only work within the highest voltage available to them. Typically they are connected to the two voltages they are shifting. Level shifters act like a switch with some power converted to heat.
Some level shifters use 'transformers' to communicate a change of voltage between the two sides. However, even these don't store energy to function, they are still acting as switches.
A DC-DC converter uses its power source to either produce a larger or smaller voltage. A DC-DC converter stores energy in the capacitor. When it's creating a larger voltage, a DC-DC converter can step well beyond its power supply voltage, unlike a level shifter.
A DC-DC converter, depending on its circuit structure, steps up a voltage, with reduced current (compared to its power source), or steps it down with increased current. Of course, this process has losses. However a step-down DC-DC converter can be much more efficient than a linear regulator.
An alternative short-term energy storage device would be an inductor.