Historically there are two main approaches to storytelling, which strike me as being heavily influenced by social class. The bards, skalds and so forth that used to entertain the royal and aristocratic courts were often known for memorising enormous poems or stories. This is not so much storytelling as it is recitation, a memorised script performed regardless of audience. Essentially hearing such a teller perform is no different from hearing an actor give a Shakespearian soliloquy... though often with less individualistic intonation and allusive inflection of the words. There are quite a few modern performers on the storytelling circuit who recite rather than tell. It normally involves an admirable feat of memory but, too frequently, erects a barrier between teller and listener ~ between eispnelas and aitas as the Spartans might have said (though maybe not with the implicit erotic frisson which that implied for the Greeks).
The alternative style of telling is to learn the plot outline, but to innovate each telling to play off the audience and integrate their reactions into the shape of the tale. A story is therefore never told in precisely same way twice, each rendition having topical, jovial additions and quirks. This style was quite probably popular in taverns and humble homes around the ancient, and not so ancient, world.
As suggested, recitation tends to be more of an upmarket entertainment largely because it involves a deal of effort (and usually literacy) which must be paid for, but also because it is safe. In performing before monarchs, aristocrats, hierophants and the like one is usually dealing with enormous egos with tissue-thin sensitivities and the kind of ribald, humorous, frequently subversive telling that goes on round the humble hearth is liable to get one's tongue cut out ~ the fate imposed on tellers by Tsar Alexei Mikhailovich in the 1600s. A known script is safe.
Having said that rigid recitation is an upper class entertainment, William Dalrymple found that illiterate bhopas (Indian storytellers) managed to memorise such massive works as the Mahabharata and recite them verbatim to their peasant audiences. However, what starts out in one stratum of society can often migrate into another. It’s also worth, perhaps, distinguishing between a sacred scripture and much more flexible folklore.
Within a modern pagan context the tension between recitation and telling also exists, perhaps more markedly in the reconstructionist camp, where arguments can break out over which version of a myth is the correct one, and the love of dressing up in quaint costumes goes hand in glove with a wish to preserve in amber, to recapitulate what was, what is known and safe, rather than to allow for the possibility of the growth of new myths, of the Gods and other spirits interacting with people in the 21st century and forging new tales... maybe no longer of kings and warriors and humble woodsmen, perhaps these days of doctors, mechanics and (Loki spare us) call centre operatives. So ready yourselves for new, innovated myths of Hades riding the London Underground and Aphrodite utilising dating websites!