What defines the outcome of the fermentation? You put the veggie, fruit in an anaerobic environment and you either get "Alcohol fermentation" (ethanol) or "Lacto fermentation" (lactic acid). What is the different input to make the different output? I know the key difference is the saccharomyces and lactobacillus. But what decides which of them start the party? 
The factors that decide what starts the party as you say are the starter and the environment. The yeast and bacteria are already present. If one of them is in the majority, then they'll get a head start without any intervention. It's just survival of the fittest. But for the most part, fermenters intervene. We add starter cultures for one, and we control the sugar, salinity, and oxygen for another. Yeast are everywhere. They love sugar and oxygen, but don't need oxygen. Yeast ferments typically start with sugar and oxygen. Lactobacilli are strictly anaerobic, and can thrive at higher salinity and acidity than yeast, so a ferment that calls for salt is often lactobacillic. Acetobacter feed on the alcohol produced by yeast but require oxygen. So if you want alcohol, add yeast starter, sugar, and let air in at first. Then cut the air off before acetobacter start taking off. If you want vinegar, leave your alcohol ferment open to the air. If you want a lacto-ferment, add a starter (or not. These are easy.), salt, and no air. That's basically it. 