Good answer daRock. Also, the datum line is the "reference line" that all other lines and measurements are compared or measured to in the profile view on the plan. So if you need 1 degree of downthrust, the line through the crankshaft would be -1 degree "with respect to" the datum line. Similar story for wing and stab incidence. A centerline most often describes the geometric center of the fuselage as seen in the plan view from above.

"Waterline" is one of those archaic terms inherited from shipbuilding where the datum line is the hull's waterline by historical convention. It's kinda like engine power being measured in "horses". The word "cockpit" is even funnier. Racing yachts in the 19th century had a sunken circular area at the helm where the pilot steered the ship. It so closely resembled a cock fighting arena the nickname stuck.