This turns out to be a surprisingly complicated issue. On one hand
‘value depends entirely upon utility’ (Jevons, 1970, pp. 139 and 77, respectively). [...]
For the marginalists of the first generation, a marginal utility curve incorporated the relation between a commodity and human wants; total utility was a derived concept and corresponded geometrically to the area beneath the curve (the integral, in mathematical terms).
Gradually, it became more natural to consider utility, right from the beginning, as a a property of consumption bundle, rather than individual consumption goods. An important step in this direction was made by Edgeworth (1881). [...] Utility of a consumption basket, rather than marginal utility of individual goods, thus became the ‘primary’ concept.
On the other hand the more commonly used notion (nowadays) of von Neumann-Morgenstern (cardinal) utility isn't the same thing as the neoclassical one, but is close enough:
What is controversial is whether the utility function derived by the N-M method can be taken to reflect the true subjective utility of the individual in the sense of the neoclassical economists such as Edgeworth. A firm negative answer has been given:
"what relationship, if any, does the N-M cardinal utility theory have to that of the neoclassical utility theorists? It is generally (though not universally) agreed that there is none - the two utility measures have nothing in common insofar as their cardinality is concerned" (Baumol 1977, p. 431; see also Banmol 1951, 1958).
Baumol is right, at least formally. The N-M hypothesis does not show that the utility function derived, though predictive of the objective choice of the individual, actually reflects his subjective utility in the sense of the neoclassical. On the other hand, most practising economists are also right, at least effectively, in accepting the N-M utility indices as subjective. This is so since, as is shown below, using the same set of axioms as the N-M hypothesis, with only the recognition of finite sensibility (that human beings are not infinitely sensitive or perfectly discriminative), it can be shown that the utility function derived from the N-M method is in fact a subjective utility function in the sense of Edgeworth.
Also, the step (back) from cardinal to ordinal utility is due to Pareto
Pareto inverted, so to speak, Edgeworth’s problem: rather than deriving the indifference curves from a prior knowledge of a utility function, he did it the other way round – his ‘primary’ concept was a series of indifference curves (later to be called ‘preference ordering’) and from them an analytical description of utility (ofelimità, in his terminology) was derived. What mattered now was the index of the indifference curves, a higher index corresponding to a higher utility.
He (correctly) remarked that a surface having I as ordinate was not univocally determined: in so doing he discovered what came to be known as ‘ordinal utility’: a result that first-generation marginalists would perhaps have much appreciated!