While there are a great many different differences in wine, there is a dicotomy by which most wines are categorized, a taxonomy of sorts. Kind of like Kingdom, Phylum, Class....ect. Wine types would probably fall somwhere between Phylum and Class (because wine is always classy!).
Sparkling wine is just as it says....sparkling. Two other general terms referring to most all sparkling wines are 'Champagne' and 'Bubbly'. Now, Champagne is actually a varietal of sparkling wine. It was stumbled upon, mistakenly, the bottle that the Romans put their raw white wine in carbonated and thus was born the first sparkling wine. The French, however, perfected it into what we know to be Champagne today. It is usually used as a toasting wine, or in celebration, but can also be a compliment often found on a breakfast table mixed with orange juice to create what is called a Mimosa. Some versions of sparkling wine include: Champagne, Brut, Pink Chamagne and Sophino.
Dersert wine is, also, just as it says....wines enjoyed, often, with desert. They are, however, not restricted to desert. They are traditionally 'white' in color and often very very sweet. They have a candy like taste when they are enjoyed with a desert and are also often used in most desert sauces and drizzles. As such, obviously, they are often served with deserts but can be used as toast wines too. Some versions of desert wine include: Riesling, Moscato and Pink Miscato.
Port wines get their name in that they were found mostly on the docks of wine merchants. It was, traditionally, the wine that was left to ferment extra long OR was wine that had gone 'relatively' bad. However, French merchants, once again, found a way to perfect this wine that would otherwise be lost and we now have port wines. It has since been perfected further in the south of Spain. Now it is commonly used as a casual evening night cap or post dinner sipping wine. Some versions of port wine include: Port and Brandy (though in some circles Brandy is considered liquor more than wine).
Table wines are the most common of wines. When you think of 'wine' you are most likely thinking of table wines. They are broken into two distinct groups: red and white (some circles hold desert wines in the table wine category). They are common in both cooking, enjoying as well as complimenting meals, snacks and events. Again, these are the most common of all wines, hailing from nearly all regions of the world (everywhere by Antarctica). Some versions of table wine include: Red - Cabernet Sauvignon, Merlot and Shiraz; White - Sauvignon Blanc, Pinot Grigio and Chardonnay.
This is a type that I have 'invented' (at least the label of, anyway). These are your 'screw top' wines that are sold on most convenience store (or budget) shelves. They are a less pricey way to be 'winey' without actually taking the 'brunt' of full-on wine. As such it comes in screw-top bottles as well as boxes. Some versions of this wine include: Gallo, Turning Leaf, Arbor Mist and Fortrais.
Either way your taste takes you - please enjoy!