Subsequent political economists, including Marx, adopted and perfected Smith's ideas.
Although a common terminology was never adopted, Marx, the physiocrats and classical economists before him distinguished between two "kinds" of prices/values. 
Here, and to the best of my capabilities, I hope to show in terms applicable to all political economists, the relationship between these two kinds of prices/values.
"It often happens that many things which have actually this intrinsic value are not sold in the market according to that value". 
"There is in every society or neighbourhood an ordinary or average rate, both of wages and profit, in every different employment of labour and stock. (...) These ordinary or average rates may be called the natural rates of wages, profit and rent". 
Compare both quotes to Marx (1865):
"So far as it is but the monetary expression of value, price has been called natural price by Adam Smith, 'prix necessaire' by the French physiocrats" As Cantillon's quote shows, and against common belief, these authors were well aware of everyday price fluctuations: market prices.
Let's adopt Smith's convention: natural (Cantillon's intrinsic value) and market prices and rates.
But, what is the natural price?
"When the price of any commodity is neither more nor less than what is sufficient to pay (...) the wages of the labour, and the profits of the stock (...) the commodity is then sold for what may be called its natural price".The following figure illustrates these authors' views of natural and market prices:
|(Right-click to enlarge in a separate tab)|
Let the red and blue dashed lines be the natural prices of brand new made-in-China digital radios and of newly built identical apartments in the same building in downtown Sydney. These prices are relatively stable ("ordinary or average"), and, as seen in the previous post, somehow reflect labour times/costs. 
The crosses are the market prices and are much more volatile, which led Smith, for instance, to consider them unsuitable for long-term output measurement.
On d1 both market prices exceeded their respective natural prices. The sellers had a good day: they achieved a super-profit (i.e. the positive distances between the respective crosses and dots).
Markets, however, are volatile. On d2 only the apartment seller got a super-profit. The gadget store owner lost money
Neither situation can last long: if capitals are free to enter or abandon a market, then permanent profits or losses are ephemeral situations. The argument to ensure this is exactly the same used ever since to justify price/quantity adjustments in the longer run: super-profits attract new entrants to the industry, output grows, market prices fall, etc.
"The natural price, therefore, is, as it were, the central price, to which the prices of all commodities are continually gravitating".That is, natural prices act as, well, natural centres of attraction for market prices: in the normal course of affairs, market prices should tend to stick near natural prices. That's the relationship between natural and market prices.
In other words, the classical "natural prices" are the homologous of the equilibrium prices of modern economists.
Let's add a few parting comments.
The first thing to note is that while the overall theory presented so far is expressed in different words and to an extent is different to what modern economics considers reasonable, it's not like there aren't any points in common.
It's in the determination of natural prices that the differences will become meaningful, both among the classical authors, and in their relation to modern economics.
So, I'll admit it, I may be seriously biased and there may well be something outrageously wrong and absurd in the way old economists thought. But it certainly is not obvious to me.
 Wilhelm G.F. Roscher offers a partial list:
"the amount of the cost of production is called by Adam Smith and Ricardo, 'natural price,' by J. B. Say, prix naturel, also 'prix originaire', because the commodity at its first entrance into the world costs so much. Sismondi and Storch call it 'prix nécessaire', and Lotz, 'Kostenpreis'. P. Cantillon, "Nature de Commerce", 33 ff., understands by the 'prix intrinsique' of a commodity, the amount of land and labor, taking the quality of both also into consideration, necessary to its production" ("Principles of Political Economy", Vol. 1. 1878; footnote 630). As quoted in "Cantillon's Land Theory of Value". HET Website.
 All quotes from "Wealth of Nations", book I, section vii, "Of the Natural and Market Price of Commodities", 1776.
 "Value, Price and Profit", chapter 2, section vi, "Value and Labour", 1865.
 Incidentally, although possible, I am yet to see a mass-produced trinket equal or exceed the price of a standard, run-of-the-mill Sydney town apartment. A cost approach to pricing explains this naturally ("At all times and places, that is dear which it is difficult to come at, or which it costs much labour to acquire; and that cheap which is to be had easily, or with very little labour" here).
At the other hand, a pure preferences model of demand (as proposed by some marginalists, as Jevons), in my opinion, has difficulty explaining this, if it explains it at all.