The process of open fermentation, open tanks with wort in them with no manually added yeast, is known as spontaneous fermentation. Another term would be "wild" yeasts, rather than the domesticated strains commonly used in brewing beers like ales, lagers, etc.
To the best of my knowledge, Sherry barrels are just used wine barrels. They're all oak and while adding other complexities, they add oak as well. Different levels of char, age, and source wood(spanish vs american oak) and initial contents(sherry, bourbon, scotch(used bourbon barrels), etc) effect the character of the outcome. But they're still oak.
Open fermentation is not exclusive to spontaneous/wild inoculation. Lots of breweries brew their standard ales openly. If pitched with enough of the desired yeast it will out compete the wild yeasts in the atmosphere.
If it is just using "wild" yeasts like Brettanomyces (the genus of yeasts in lambics) but in closed, it would not be spontaneous. However, since you're counting on the atmosphere to provide the Brettanomyces, it is spontaneous. I'm aging two beers right now I brewed using Brett L and Brett B. They are "wild" but not spontaneous, as I manually added them.