At least forty twelve ;) It really depends how you’d like to categorise them... ie, dry, off dry, sweet, sparkling or fortified...
Going deeper, you have aromatic vs non-aromatic varieties... ie, Riesling has a lot of fragrance, which in turn informs its flavour profile. All it needs it a quick and coldish ferment in stainless steel and hey presto, awesomeness! Chardonnay is naturally fairly neutral aromatically, but responds beautifully to winemaking artefacts, like whole bunch fermentation, oak ageing and lees stirring in barrel.
By variety... there’s a truckload of those... hundreds... even within a single variety there can be many distinctive styles. For example, unoaked Chardonnay vs oaked Chardonnay - some would argue that unoaked Chardonnay is the work of Beelzebub, aromatically bland and flavour-limp, the kind of wine you might gift to someone who reckons Spam deserves a Michelin star. As with most things wine, there are exceptions. Some of the best Chardonnay wines in the world are unoaked; many Chablis and most Champagne are unoaked. Quality, cool climate, oaked Chardy which has been lees stirred can be strikingly aromatic, rich and full-bodied, with deep flavours of stone fruit, vanilla, butter and minerality.