iOS8 Health: Steps VS Flights Climbed VS Walking+Running Distance
You need an iPhone 6 to be able to calculate 'flights' without any external device or manual input, as it uses a new sensor, the altimeter/air pressure sensor.  


Steps is 'how many paces you took' 
Walking/running distance is your total distance travelled - but of course paces are much longer when running.
Flights is 'how many times did your elevation change by more than [I think] 12ft whilst you were walking.'


As far as I'm aware, 'steps' is included in 'flights', as the lateral component.
Walking up a hill will generate data for both lateral [steps] &amp; vertical [flights] components.