Organic

Organic:
Very simply, organic wines are produced with organically grown grapes. In order to have organically grown grapes, a vineyard manager must implement an entirely different set of practices to maintain their vines.
By the way, organic doesn’t imply that the wine doesn’t have additives. There is, in fact, a list of additives, including things like yeast, egg whites, and animal enzymes (like rennet in cheese) that are allowed in organic wines. Being organic doesn’t necessarily mean a wine is vegan.

Natural:
Natural wine is wine made without chemical and minimum technological intervention in growing grapes and making them into wine. The term is used to distinguish such wine from organic wine and biodynamic wine because of differences in cellar practices. All natural wines are, however, farmed organically at a minimum and many growers are biodynamic in the vineyard as well.
Strictly speaking, natural wines are wines that are produced without adding or removing anything during winemaking, although some growers add tiny quantities of sulfites at bottling, so that strictly speaking their wines are not natural wines, but 'only' organic (and possibly biodynamic)

Biodynamic:
The concept behind biodynamics is that everything
in the universe is interconnected and gives off a resonance or ‘vibe’. The interconnectivity of everything even includes celestial bodies like the moon, planets and stars. Biodynamic viticulture is the practice of balancing this resonance between vine, man, earth and stars. Essentially, biodynamics is a holistic view of agriculture.
Biodynamics occur primarily in the vineyard before winemaking even happens. All the various tasks, from planting, pruning, to harvesting, are regulated by a special biodynamic calendar. The calendar was originally devised by the ‘high priestess’ of Biodynamics,
 Maria Thun, who divided days into four categories:
 Root, Fruit, Flower and Leaf Days.
Each biodynamic calendar day coincides with one of the four classical elements of Earth, Fire, Air and Water
 that have been used since before Plato’s era:
Fruit Days: Best days for harvesting grapes
Root Days: Ideal days for pruning
Flower Days: Leave the vineyard alone on these days
Leaf Days: Ideal days for watering plants
Besides the biodynamic calendar, no chemicals or ‘manufactured’ additions (like commercial yeast) are allowed in biodynamic wine. Instead, wine growers make special compost preparations with natural ingredients to bolster their vineyards.