Good question! I believe the majority of choreographers use a combination of already learned steps and motions deriving from their teachers, and then put together into the specific dance style. Most have their origin in Classical ballet. Then each modern style makes variations of for example pliés or how we use the hands. In Ballet our fingers should be held together, thumb slightly hidden but perhaps allowing the pinky to show a little. In Jazzdance, especially Showjazz (dance in musicals), the fingers can spread in a certain motion developed by Bob Fosse, who in turn taught one of my old teachers in Malmö, Sweden for the famous dance called All that jazz! among others, whereas Isadora Duncan has "spiritfingers" elongated when running across the floor allowing the motion to continue through the air. In Hawaiian Hula it certainly is a requisite to have lovely soft hand motions to share a story to entice the audience with its feminine beauty. And it's in the two latter, and Westafrican dance, the choreographies are instead made more intact, passed down through generations and with some added renewals.
It is always an interpretation and/or addition to the selected music. Most Modern Contemporary teachers want the dancing to the music be in a dialogue to the melody, in comparison to ballet and jazz where the dancing is more directly to the beat, on point. Art and entertainment. Jazzdance in turn, also has influences from African dance through the beat of the drums forming different rhythms. These different beats later became the foundation for rap and streetjam, formerly known as Breakdance then later hiphop and Street with their own variations.
Each teacher also has their own personal style in teaching and doing their motions in terms of expression, emphasis and variations. A dance class however, is consisting of the same everywhere: warm-up for an hour, technique exercise often on the diagonal for fifteen minutes and then a choreographed piece of a couple of minutes (such as 8 x 8's), hardly a whole song in one class, for the last fifteen minutes. For me personally, I prefer to do the same routine for three classes to make it really sit. In this practice, we can lean on something called "muscle memory" which is our own bodies way of forming and reacting in certain ways, that we as dancers can use, especially on stage. Once performed in front of a live audience, it sticks forever! In this also lies real mindul presence without cameras in our faces and all the retakes already done in practice. Repeat, repeat, rehearse!
In Hawaiian Hula and African dance, we dance to the whole song and let the music lead the motions more than the other way around. Dancing Isadora Duncan has its resemblance since many of her original choreographies are danced to short classical tunes of just a couple of minutes, and often in group dynamics that enable us to form, enter and exit the stage in a clearly defined routine already in the first practice.
Sometimes when we dance and feel free enough in our own bodies, it will lead us into an original motion that comes naturally as a way of expression and thus this is when the real creation starts. (I think I have been able to come up with three so far in my entire life.) As with every piece of art, we should always be able to cite the source and distinguish which is which and make sure the original work is respected consecutively when able, such as with Hawaiian Hula and Isadora Duncan who keep their protocol. Too much improvisation usually is the result of not being able to memorize or perform the actual choreography, unless it is the aim of the exercise such as in dancing 5rhythms as developed by Gabrielle Roth and later Ecstatic dancing which is to liberate us from stressful tensions.
We can either consciously decide what each step counted for and put together in a certain order should be, or we can let our bodies lead in flow trusting it to express that which is coming from within when we hear certain music. It is this coming from within that must be more respected and protected as personal, just like with words in Writing, in creating a choreography that can be repeated.
The show must go on!
Photo, courtesy of the Merrie Monarch Festival 2016.