Why The extended double Zepp is two collinear elements of about 0.64 wavelength each fed in phase at the center, giving a total length of roughly 1.25 to 1.28 wavelengths. That is the longest a collinear pair can get before the broadside lobe starts splitting, so it delivers about 3 dB gain over a half-wave dipole broadside to the wire. Because the feedpoint impedance is high and complex, it is normally fed with open-wire line and a tuner.
Watch out The 1.5-wavelength center-fed choice is a different antenna: at that length the broadside lobe has broken up into multiple lobes, which is exactly what the extended double Zepp stops short of. The end-fed options describe the original single Zepp idea, not the extended double version, which is center-fed.
Double = center-fed (two halves), extended = stretched past 1 wavelength to about 1.25 for extra gain.