European's "Customs union" and "Single Market" what's difference?

WHEN discussing a “hard” or a “soft” Brexit, commentators regularly talk of the European Union’s “customs union” and “single market”. 

Currently Britain is a member of both. It is possible to be a member of just the customs union but not the single market (look at Turkey, Andorra or the Isle of Man). Conversely, it is possible to be a member of just the single market but not the customs union (take Norway or Iceland). Often the two terms are elided (to leave out of consideration), which has the effect of concealing important differences. What are they?

A customs union is a type of free-trade area. Two or more countries agree to abolish (to end the activity or custom) restrictions on mutual trade, and to set up a common system of tariffs and import quotas that apply to non-members. In the jargon, they have a “common external tariff” (CET). The EU, for instance, has a common 10% tariff on cars imported into it. The main advantage of a customs union is understood when you consider what happens when there is no CET. If France had zero tariffs on Japanese whisky, but Britain had a 10% tariff, then it would be a profitable wheeze (old fashioned, informal - clever and often unusual idea or plan, especially one that is intended to achieve a profit or some other advantages)  to export Japanese whisky to France, and thence (from there) (freely - without paying tariffs) to Britain. So Britain would have to carefully monitor whisky imports from France, and slap (to froce a rule, tax or punishment to be obeyed or received) a tariff on any Japanese stuff sneaking (to go somewhere secretly) in (so-called “rules of origin” regulations). With a CET, however, such monitoring is no longer necessary (because the possibility of such arbitrage is eliminated). One disadvantage of a customs union, however, is that its members are not allowed to negotiate their own trade deals with third countries. 

What of the EU’s single market? It is sometimes called the “internal market” and was once called the “common market”. This is another type of enhanced (to improve the quality, amount or strength) free-trade area, though for a different reason. Not only do goods move freely, but so do services, investment and people. To achieve this much more ambitious goal, the EU needs to get involved in harmonising regulations across the single market. This is why there are much-maligned (intended to cause harm) rules on, for instance, the efficiency of vacuum cleaners across the EU. In the absence of such regulations there would be a regulatory race-to-the-bottom: countries would compete to produce the cheapest-possible vacuum cleaner across the EU, sacrificing safety in the process. It also explains why there is free movement of people: this allows for the exchange of typically non-tradable goods, such as plumbing. 

With all this in mind, what should Britain do? 
It is possible to be a member of the single market without being an EU member. The European Economic Area (EEA) agreement leaves three countries (Norway, Iceland and Liechtenstein) in such a position. They are not part of EU customs union and thus free to strike their own deals (but, remember, they need to abide by complicated “rules of origin” regulations). If Britain however decides to quit the single market, there is no point in being part of the customs union; quitting it would allow the British to strike their own trade deals. The best option from an economic perspective, of course, is for Britain to quit neither the single market or the customs union. But then that wouldn’t be Brexit, would it?