Which element of a vacuum tube regulates the flow of electrons between cathode and plate?
Why In a vacuum tube the heated cathode emits electrons that are attracted to the positively charged plate (anode). The control grid sits between them and its small negative voltage swing steers, or throttles, that electron stream, which is how the tube amplifies: a tiny grid voltage change produces a large plate current change. That is the same role the gate plays in a FET.
Watch out The screen grid (in a tetrode) mainly reduces grid-to-plate capacitance and stabilizes plate current, and the suppressor grid (in a pentode) pushes secondary electrons back to the plate; neither is the main current control. There is no 'trigger electrode' in an ordinary amplifying tube.
Control grid controls the current. Grid = gate of a FET; screen and suppressor are just helpers added later.