14 AWG refers to the overall size/area of the conductor. However a 14 AWG flexible cable comprises of multiple strands of finer wire. If it is a few thicker wires then the cable will be stiffer. If it's a lot of smaller wires then it will be more flexible.
In European terms this is normally indicated by a number and the size of the individual cores e.g:
6 mm² CSA , 84/0.3 mm will be alot more flexible than 6 mm² CSA , 7/1.04 mm
(note that in the "7/1.04 mm" part the size refers to the strand diameter)