Change of wire and or number of windings will affect the electrical impedance. For the low frequencies the DC-resistance will dominate but at higher frequencies the inductance of the coil will dominate. This means that the balance between low and high frequencies can be adjusted within some limits. Basically the vibrator needs current to vibrate, so lower impedance means higher vibration force level (VFL). A battery-driven device will therefore be limited in performance by the available current.
The moving mass
The BEST vibrator is a recoil device, meaning that the moving part of the generator will cause a recoil force on the housing which then will vibrate. The mass of the moving part has direct influence on the low lying main resonance peak and the frequency response in the region. But the mass also has direct influence on the maximum VFL for low frequencies. An extra mass element is used to adjust these properties.