- Is it a dipole or monopole antenna? I see only one conductor, so I'd say it's a monopole. But, where is the ground plane? As far as I'm concerned, a monopole antenna needs a second metal object in order to radiate.
The first image that you've attached is a rubber-ducky monopole antenna. An open-ended transmission wire (line) when excited/driven by an AC voltage source does act as a radiator but just not efficient. When you bend the two open-ended wires to a certain length, it performs better. The oscillatory voltages and currents produce oscillatory electric and magnetic fields. When the effective bending length is a half-wavelength, it performs still better and there is maximum potential difference at the edges. Current is maximum at the center.
Coming back to the Wi-Fi antenna: consider a quarter wavelength monopole antenna. One of the open ends is grounded and the other end is a quarter wavelength long. Excitation is the same, an AC voltage source. But in this structure, the maximum potential difference at the edges is half of that in the case of a half-wavelength 'dipole'. Consequently, there is not strong enough E-field as in a dipole but this is sufficient.
The first image is of a monopole antenna and its radiation pattern is shown in the following figure. It has an omnidirectional radiation pattern, resembling the figure of the number 'infinity or a dumb-bell'. The mobile phone Wi-Fi antennas are low profile patch antennas embedded onto a substrate and fed internally.
- I don't see even the metal conductor, but only a plastic monopole. So, I'd think that the inner part is a conductive monopole. But why is there such a plastic external shield?
Yes. The outer shielding may be for protection against damages. This may be thought of as equivalent to a 'radome' present with parabolic reflecting structures.