It's not really a short form is it? 'Charlie' could be classed as an affectionate or familiar form of 'Charles'. However, at the other end of the spectrum, it could be used in a diminutive or scornful manner. As when people refer to Prince Charles as 'Charlie'.
people do say "charlie,short for charles" though dont they! my friend called her son Henry and lost count of the number of people who asked was he going to be Harry for short................erm no actually cos that is the same length as Henry
yes, it's a familiar form, which means you use it with someone you're familiar with - someone in your family (which is what familiar means) or close friends. Versions of names that end in a Y sound are often used for children - Billy or Willy for Bill or Will or William - so they have a slightly condescending air to them. Call Prince Charles Charlie and it seems you're sneering a bit.
i have to agree with you pollyspeed my son is called harry and over the years many people have enquired as to whether his actual "real" name is henry!! my daughter is called charlotte but has always been referred to as "charlie" as it's easier to roll off the tongue day to day and she only gets referred to as charlotte when she's in trouble!! lol :-)