Story telling is different from Drama or solo/mono acting...it is an interactive process where the audience is asked to move with the Teller, imagine with the Teller, and experience with the Teller.
There are many others qualified to give an insight on these differences, but I speak from my thoughts/heart.
For those who enjoy performing arts this is a very genteel art to pursue. I call it that because, there is no right or wrong way to do Stories.
The only way is to connect with your audience. To share with them a thought, a feeling, an experience.
With younger children it is important to have a story line, as they need a plot, an organized thought process, which they themselves may not have in their thoughts.
While with an audience that gets older, you don't need an organized plot. You need to spark imaginations,and even give them an opportunity to make their own endings, extract their own conclusions.
Yet there are some Learnings that I have gained from my own meager experiences in story telling:
a) Don't tell till you are sure about the acoustics. Problems with the mike or the sound system is the first step to not connecting with your audience...and it's not worth having a bad feeling at the end of the session, when you know it's not you but the technical part that has slipped
b) For smaller and cosier groups, go in for an enclosed space, especially when there is no mike and you have to rely on voice,
c) Eye contact and smile...connect with your audience, move with them, include them, share yourself with them,
d) Have no inhibitions! A teller who is comfortable is loved the most.
e) Believe there is no right or wrong in this, it is a process of Sharing, and the most wonderful aspect of the telling,
f) Choose your story well, age, interest and environment plays a crucial role in this
g) If the environment is not conducive to the telling, you cannot connect with the audience...
h) Brief the hosts. Puppet shows require greater involvement from adults to keep the audience from getting up and trying to see behind the screen(!) (Happened to me). So you need an adult to keep the kids from peeping behind!
i) Puppet shows and Story telling are very different, and people usually expect a puppet show when you say Story telling, so make that very Clear!
j) Telling a story, visualizing a story for an audience is different from Reading a Story! The Teller needs to recreate the story, add her own imagination, thoughts and feelings, and improvise the story with out taking away from the story. I would even say this, the Teller has every right to make additions and deletions, in order to convey her message, her thought to the audience.
k) While as you Read a story, it is only right for the Teller to convey exactly what the writer has expressed in words.
l) So Story telling is an improvisation, an adaptation of a plot, a manner of sharing creative verbal imagery!
The end product may be very different from what you shared with a different audience, at another time!