Perhaps those who "confuse" these two terms do so because they've taken an economics course and realize that there are no superior definitions of "worth" than "what someone values an item at".
Taking a single economics course is a sure way to pollute your thinking about what value is.
The idea of "worth" or "value" precedes economics as a discipline. Vulgarized economics might offer really weird and ideological versions of them, but it can't demand that everyone stop using them as normal people do.
Anyone can think of instances where someone at their company performs better than someone else but is not well-compensated, relatively-speaking. But no one seriously thinks that someone is inherently more valuable just because they're paid more.
If you think about it, anytime you buy a stock or engage in a market transaction you're rejecting the idea that the price of something is its value. If you exchange money for a good, what you're saying is that that good has more value to you than the price you're paying. The person you're bargaining with thinks the converse. Or if you're purchasing an equity, what you're effectively saying is that you have some non-public knowledge that that equity has more value than what the market price suggests (if you buy equities on a different basis, you should probably stop and move to index funds).
In Groupon's case, its econo-speak "value" came about because everyone assumed that they could gamble and win on the theory that there's someone who's making the same assumption that they could gamble and win on the same theory as them but who is slightly less savvy. Just because a bunch of people are collectively changing their minds about how many idiots are out there who are slightly less savvy than them doesn't change the actual value Groupon ever had.
The micro-level counter-examples you provide for macro-level mechanisms simply don't work.
If you consider your first example at a market level, people that are better compensated are more valuable—because they create more value (the discussion is—of course—not around one's value as a human being). The only reason for imperfection in this regard is market friction—which there is a lot of, in every market. But the market value tends very quickly towards the real value if the market is liquid enough.
In a liquid equity market (stock exchanges for example), the price of the stock you buy is its current value. However, you are making a bet on the future value gains of the company. Buying stock for its current value is investing; anything else is speculation.
That is a very practical definition for economic models but that doesn't make it complete. Your link says value within a market, and a single offer for a company by Google does not automatically qualify as a market and therefor determine value. If it did, I could pay you 1 billion dollars for a rock and it would be "worth" 1 billion dollars. I prefer to think of it as, given imperfect information and an inability to predict the future, market value trends towards true value, where true value is a fuzzy subjective set of ideals held by individuals and society.
Just because one person values something at a number doesn't mean anyone else (or enough other people) do. The price of their shares tell you the "Current Market Value," but they don't tell you what it is worth in the long term.
Things are only worth what the next person is willing to pay for them, not what the last person actually paid. People buying the Groupon IPO were mostly going with the "greater fool" theory of investing. A money losing company with lots of accounting issues is not something that generally just goes up and up in value.
>> they don't tell you what it is worth in the long term
This reminds me of the Keynes quote: "The long run is a misleading guide to current affairs. In the long run we are all dead."
More on topic, the long run as an abstraction is limited in its utility for investors. This mostly because investors (like gamblers at a roulette wheel) have to place their bets while the wheel is spinning. Without taking a position on GRPN, I'd say that the "long run" verdict is hardly in at this point.
Anything is only worth what someone will pay for it. There's no other meaningful definition. If Google was willing to buy the whole thing for 6 billion, it was worth 6 billion. It only gets questionable when you start buying and selling shares rather than the whole thing.
The other meaningful definition of worth is the inherent value of the object. A ION bracelet or Rawlings Power Bracelet may be sold for $30. But the plastic or metal in the item is actually worth $2. Or the fact that someone now believes they have better balance may be worth $2,000 to them, but the metal and plastic costs $2.
If you think there's a meaning to the phrase "inherent value", try to define it instead of being petulant. Nothing has value without some customer who has a demand for it, which is why the concept of inherent value is meaningless.
If something was only worth the cost of the materials that went into it--then what determines that cost? Even steel and oil have value that depends on customer demand rather than any sort of inherent value. And if that was all it was worth, why would you waste time and effort turning steel into a steel bracelet, or a steel ship, when the end product wasn't actually worth more than the materials that went into it? You'd waste energy and human effort without producing any value. You'd be richer just holding onto the raw steel itself.
Perhaps we could draw it as the difference between "would pay" and "paid".
You can put a price on something, but until someone has paid it, it seems difficult to argue that the thing is "worth" your price... to anyone. But people routinely argue this, and others believe them.
But that is what the stock market is: A constant and immediate recalculation of worth.
To take another example: Facebook obviously, at the time of IPO, was not worth what it sellers hoped it would be. At some point in the future it will be worth much more than it is today, and at some other point it will be worth nothing. Today, the agreed worth/value of one FB share is $27.
