Calligraphy is defined as: decorative handwriting or handwritten lettering.
There are some scripts that follow certain rules for spacing and drawing the letterforms, and then there's modern calligraphy. Modern calligraphy is unique to each calligrapher and is a style that is personally developed. Some calligraphers develop "bouncy" styles, while others may have more of a whimsical, airy look.
Styles that have defined rules and look similar from one calligrapher to another include copperplate / engrosser's script, spencerian, italic, Roundhand, uncial, and so many more. Most calligraphers make these styles their "own" by incorporating special flourishing or using certain variations over another.
example of Italic, left, and Spencerian, right
The next time you're looking for a calligrapher, be sure to ask which script style(s) they specialize in!