Antenna's have a rated bandwidth of frequencies on which they operate. I understand that the antenna will still operate outside these frequencies, just that the signal will experience a greater attenuation at frequencies outside this range (like a filter's passband). Hence, my question is not a duplicate of this onethis one.
What physical factor affects the bandwidth of an antenna? Is it the material? The image below shows two SMA compatible antennas. Both are almost the same length. The shape of the grey covering of the second antenna suggests that there is a similar inductor like structure inside it, which I know from practical experience is the "gain" of the antenna (correct me if I'm wrong).
The grey antenna is for 2.4 GHz WiFi while the black one is for sub 1 GHz GSM.
I can't seem to find out what physical factor affects the bandwidth. The only option left seems to be the material. Is it the case?
Also, since both have the same shape, is it safe to assume that both of them have the same polarization and radiation pattern? (I'm not good at Physics, avoid downvoting me on this). I don't know the model of any of these antennas however a Pulse W5017 antenna (not shown here) with the same shape has an Omnidirectional polarization and a Figure-8 radiation pattern according to it's datasheet (also shown below). Is it safe to assume that these antennas will have it likewise?
Radiation Pattern of identical Pulse W5017: