Stirring and shaking of the same ingredients will yield different results. A shaken drink will be much more aerated than a stirred drink. Some have said that the decision whether to stir or shake should be made based on the presence of certain ingredients, such as citrus juice. This approach seems to be based on the ‘one-size-fits-all’ approach to amounts for citrus juice exhibited by the modern ‘call-‘em-all-cocktails’ crowd. It ignores the different desired results for the different genres of drinks, which should be informative as to when and and why citrus juice should be used only as an accent. The only type of ingredient that demands shaking, regardless of the genre of drink being made, is the thick element.
Virtually all slings (including true cocktails, of course) that are not simply built or churned should be stirred. This allows the alcoholic base of the sling to be the standout star of the drink, as is desirable and essential to that type of drink. Stirring will harmonize the other ingredients with the strong element, without subverting its nature. The only exception to this rule for the sling genre is when the drink is to be thickened, such as in the case of the Alamagoozlum Cocktail. When a sling is shaken, the result is that too much of the character of the alcoholic base is lost to ‘bruising’ (the violence and aeration done to it while shaking). To demonstrate the real effect of bruising, make two original Martini Cocktails (1 fl-oz. tom gin + 1 fl-oz. sweet vermouth + 2 dsh. orange additive bitters), but shake one of them instead. Taste for the resulting loss of appeal found in the shaken one, and you will know what bruising really means. Alternatively, this same test may be done with the original Bronx Cocktail from 1908 (2/3 fl-oz. Plymouth gin + 2/3 fl-oz. sweet vermouth + 2/3 fl-oz. dry vermouth + 2 dsh. orange additive bitters + 1 barspoon orange juice), one properly stirred and the other shaken. Then you will discover directly through your palate why it is not always correct to shake a drink just because there is citrus juice in it.
Virtually all possets that are served cold should be shaken. That is because, by their nature, possets are led by the thick element. The thick element usually needs shaking to aerate and emulsify it, and to incorporate the other ingredients into its thickness.
Virtually all punches that are not batched or swizzled should be shaken. In the case of punches, the ingredients should be balanced in the finished drink. Since the alcoholic base is not the standout star in any punch, shaking and aerating is desirable to create a harmonious balance of the ingredients.
Virtually all succulents that are served ‘up’ (the blossoms, mainly) are to be shaken. With such significant amounts of succulent juice, there is simply no way to make the alcoholic base in a succulent the standout star of the drink.