Arabic calligraphic scripts can be divided into two great families: the so-called rectilinear scripts (Kufic), and the cursive or round scripts. Although Kufic is too often presented as if it were a single, specific script among the rest, that is a mistake, and it can be only be reduced to a formula in an artificial way. To clarify this, I will briefly describe the respective history of these two families and explain their fundamental differences. (Note that all the names by which we designate the scripts are applied in retrospect. Period sources used them more fluidly if at all.
The round scripts are called in Arabic al-khatt al-mansûb, which is "the script that conforms, that is regulated". That is the main difference with Kufic: the round scripts are formal. There are very specific rules to write each letter and connect them together, rules to be practiced till the hand follows them automatically.