What is the difference between "Collector-Emitter" and "Base-Emitter" Saturation Voltage?
Vce(sat) is the voltage measured at the collector relative to the emitter under the specified conditions (say 150mA of collector current flowing, and 15mA of base current applied (forced beta of 10, obtained by dividing Ic by Ib thus 150 over 15 mA).

Vbe(sat) is the voltage measured at the base relative to the emitter under the specified conditions, as above. 

So if you are wanting to switch a 150mA load under those conditions with (say) a 10V input, you will use the latter number to determine the required resistor value to get the minimum base current needed (and ensure you don't exceed any maximum if the minimum Vbe(sat) is specified).