What is the difference between a pitot tube and a pitot-static tube?
A pitot probe strictly measure ram air pressure, commonly called "pitot pressure" or Pt pressure. A pitot tube measures pitot pressure and pitot pressure only. A separate static port is required to measure static pressure (Ps) and will usually be located on a section of the fuselage where airflow is minimized.

A pitot-static port is a combination pitot AND static port. That is, the tube itself has an opening for detection of Pt pressure and one or more openings for static pressure. In this case, there generally is no static port on the fuselage since it's built into the pitot-static probe. 

TLDR: the only difference between the two is that a pitot-static probe is a pitot probe with static ports whereas a pitot tube is strictly just a pitot tube. :-)

Edit: Not sure if the original question was edited after my answer or if I missed the second part in my original response... Static pressure is required to know indicated airspeed because as altitude increases, airspeed increases due to less air resistance.