AC current terminals
Why do we have one constant positive terminal that keeps lighting up a tester


AC mains have a 'live' terminal not a positive terminal. And the voltage at live terminal varies sinusoidally in between  -ve voltages and +ve voltages with respect to the neutral line at a rate of 50Hz. So the intensity of light also changes with this voltage variation. But because of persistence of vision, human eye can not detect this variation. Eye will perceive it as a constant intensity light (whose intensity will be about average of the original varying value).  

In short, the inability of human eye to detect 50Hz variation creates an illusion of constant light. 


  Why no electric shock?


Tester uses a neon lamp inside it \$^{\mathrm{[source]}}\$.  The neon lamp takes very little current to light, and thus can use the user's body capacitance to earth ground to complete the circuit. This small current won't be a problem for human body.   

In short, the high resistance offered by tester limits the current through it reducing the chance of electric shock.