In short the drinks you've listed are all alcoholic beverages and fall into 4 categories:
Wine,
Beer,
Spirits and
Ready to drink mixers (RTD's).
Let's start with ALCOHOL itself:
There are 4 types of alcohol: ethanol, methanol, propanol, and butanol. Only 1 type of alcohol (ethanol) is safe for human consumption. This is the type of alcohol found in alcoholic beverages. Ethanol is one of the byproducts of yeast metabolism which we call fermentation. In simple terms, yeast consume sugar to give them energy and they produce carbon dioxide (CO2) - just like we do! But unlike us, they produce alcohol as well.
The CO2 produced by yeast is seen every day as the 'holes in your bread' or the bubbles in your beer or champagne and of course the alcohol is what puts the 'adult' into adult drinks!
The origins of alcoholic drinks roughly fall into two main categories:
Wines and Beers.
Wines:
Simply put, wine is the fermentation of sugar from fruit. Whilst it can technically be made from any sweet fruit, the term wine generally refers to alcohol fermented from grapes or grape juice unless some other fruit is specifically mentioned. Fruits are high in fermentable sugars (glucose and fructose) so the yeast can happily go to town on the fruit juice so long as the other conditions (like temperature, toxins, pH) aren't too unfriendly.
Beers:
Beers are the fermented product of sugars obtained from the breakdown of complex polysaccharides - starches. A starch is basically a long chain of simple sugars all joined together and is the main form in which plants store their sugars for later use. Before the yeast can get at the sugars that are tied up in the long starch chain, it needs someone else to come along and break down those starches. This helper comes in the form of an enzyme which can dismantle the starch into the sugar molecules that the yeast needs to feed on.
In this day and age, we can manufacture the enzymes we need to do this, but many brewers still use the old fashioned method of malting some or all of their grains in order to use the seed's natural enzymes to do the work for them. Other methods include prolonged boiling of the starchy base material (as in tequila and mezcal), the use of a fungus (like koji used to make sake) and in some ancient tribal alcoholic drinks the starches were actually chewed to start the conversion process - human saliva contains the enzyme amylase which starts to break starch into sugar before you even swallow your mouthful of potato!
Once the starches are broken down into sugars, the yeast can do its thing and fermentation proceeds as for wine.
It's interesting to note that based on this definition, sake - commonly called rice wine - is actually a beer as is the base alcohol for whisk(e)y!
Spirits:
Beers and wines are essentially a primary process. Producing a spirit is a secondary process since you need to start out with a beer or a wine to begin with. Spirits are produced by distillation - separating the alcohol and some of the more volatile (easy to evaporate) components of the beer or wine and leaving the heavier flavour and colour compounds behind.
The aim here is to concentrate the alcohol and in fact, in commercial vodka production, this is done to the point of separating ~96% pure alcohol from the original mixture of 5-15% alcohol. The other 4% includes some water and traces of other volatile compounds called congeners- things like esters, and other alcohols. Other more flavourful spirits are distilled to lesser purities in order to keep some of the character of the base material.
Every style of spirits comes with it's own set of rules which govern what it can be called, how and where it can be made and how it has to be aged.
Vodka is the most neutral of the potable spirits and not much is done other than dilution to bring it down from the 96% pure spirit to the ~40% product that you buy at the liquor store. It also has the least rules for its production - it can be made from just about any base material, it can be made just anywhere and the only real stipulation is that it should be neutral in character.
Gin is basically vodka which is redistilled or infused with juniper and other botanical flavourings. While are various types of Gin, some of which can only be made in certain places and/or by certain methods, it can also be made from a wide range of base materials.
Mezcal is the national spirit of Mexico and is solely produced using traditional methods from the heart of the Agave plant. Tequila is a specific type of mezcal made from at least 51% Blue Agave and can only be produced in 5 Mexican States. (Tequila cannot contain anything other than Agave, water and maybe a little caramel for colour which means if it has a worm in it - it's not Tequila, it's Mezcal!)
Brandy is distilled from wine. Most brandy including Cognac and Armagnac is distilled from wine made from grapes although there are many eastern european examples of fruit brandies from the likes of plums, cherries and apricots. Some brandy, like grappa, can also made from the skins left over from winemaking. Brandy is produced all over the world and most culture have their own rules about what methods can and can't be used.
Rum may only be produced from the product of byproducts of cane sugar. Rum Agricole is made from raw sugar cane and all other rums are made from various form of sugar or molases from the refining process.
Finally, Whisk(e)y is the product of fermented grains: barley, wheat, corn etc. The specific grains used differ according to the local rules of the various styles. Scotch, Irish, Bourbon, Tennessee, American and Canadian whisk(e)y all have specific rules about how they must be produced and matured. Other countries and styles tend to be a little bit more open to interpretation.
RTS's:
Ready to Drink (pre mixed) drinks, like breezers, are basically a spirit which is premixed - usually with carbonated water, sugar and flavourings - to produce a mixed drink which can be drunk directly from the packaging. Breezers, for example, are based on Baccardi rum with essentially carbonated water and cordian.
