To answer the question more specifically, YES, the length of the antenna does matter. The length of the antenna is proportional to the frequency being used (transmitted or received); hence, the designations 6M, 2M, 70cm, etc. These are the full length of the antenna for the frequency in that range (band). However, usually, a size different than the full wave length is used, i.e. half wave or quarter wave, because it would be impractical to use an antenna at its full length. The antenna is cut down in a ½, ¼, 5/8 or other size to shorten the length for mobile use. Most base antennas use the full length because it is much easier to mount a larger antenna on a mast.
However, the size of the antenna is not as important when receiving, as opposed to extremely important when transmitting. The key is to get an antenna close to the size to match the frequency you are trying to monitor, whether full wave or fractional wave. As mentioned, some antennas incorporate the ability to receive (and even transmit) on multiple bands. The lower the frequency, the longer the antenna; the higher the frequency, the shorter the antenna. Theoretically, you would want an exact match (antenna size to frequency match) for each band to which you are listening. Professional radios have specifically tuned antennas to match the freqeuncy it uses.
I remember when I was a kid, I used to stick a hanger in the back of my black and white TV to get a reception because the telescoping antenna was broken – and no, I am not that old, it is just what my parents could afford to get me; I felt privileged to have my own TV in my room.
The black plastic thing in the middle, called a coil (or center coil if it is on the center of the antenna or base coil if it is on the base of the antenna) is actually wound up wire to make it so you do not have to have a, say, 2 meter (6 foot) long antenna, but a much shorter antenna with much of the length wound up in the coil. Some antennas have more than one coil.
If you actually took apart many rubber ducky antennas, the wire inside would be wound up like a spring; the wire is much longer than the length of the rubber or plastic shell. That is why most VHF radios have a somewhat short FAT antenna, the antenna is actually much longer, but wound up inside the plastic/rubber shell; and a UHF is much thinner and slightly longer to the look, but in reality, much shorter. It is a matter of practicality and aesthetics.