I believe the right most antenna is a mono-pole helical "rubber ducky" (please correct if wrong).
But what type of antenna is on the left? It is terminated with a U.FL connector (not shown) and the center pin connects to a thin copper braid covered in a transparent insulator. The metal spiral connects to the shield and is conductive but I'm not sure what type of metal it is.
Both antennas have had their rubber moldings removed. They are both made by Wellshow but I can't find details of the left one. I do know they are both made for 900/1800MHz.
Best Answer
As far as I can see that's a Helical Antenna on the left too. Helical Antennas are directional antennas.
See Wiki for further informations.
However it's a special helical antenna. Do to its small size they make some tricks:
There's a paper about it here (whitch is the above's citation's source).