It was recognized as an intangible quality of persons in economics back to at least Adam Smith. He distincted it (as "enterprise") from labour (economics) which can be coerced and is usually seen as strictly imitative (learned or transmitted, via such means as apprenticeship).
Marxist economics refers instead to "an individuals social capital - individuals are sources neither of creativity and innovation, nor management skill. A problem with that analysis is that it simply cannot explain the substitution problem and lack of demand that occurs when, for instance, an understudy takes on a leading role, or a second author takes over writing a popular book series. At the very least there must be some conditional, if not firm-specific then "class specific, special ability to command premiums for outstanding personal performance.
Neoclassical economics by contrast refers to "the individual in whom the human capital is ... embedded", which implies a strong association of the individual with the instructional capital they learn from, with little or no social capital influence. This is orthogonal to the Marxist view, but not necessarily opposed.
Human development theory reflects both distinctions: it sees labour as the yield of individual capital in the same way that neoclassical macro-economics sees financial capital as the yield of the looser idea of human capital. But the rest problem and social welfare function selection, as well as the subjective factors in behavioral finance, has led to a closer analysis of factors of production. In effect, the financial architecture is no longer trusted as an arbiter of the value of life as it was in neoclassical economics. Money is not seen as values-neutral, but as embodying a set of larger social choices about money supply rules, made by measuring well-being of whole populations.
Fusions of terminology are common. Sociological analysts refer to "individual-level elements of social capital" or "an individual's social capital" or just "individual social capital" while economic analysts often use the phrase firm-specific human capital. In either case the clearly includes individual capital but also some "activity-", "community-" or "firm-specific" social capital (community trust) and instructional capital (sharable knowledge or skills). This is easy to measure: its yield is your salary in your current job.
To the degree this is consistent if you take other work nearby, this opens the questions of what is not "firm-specific" and whether a nation is just a bigger "firm": Some analyses see political capital, or just "influence" or "trust of professionals" as a full style of capital of its own. Some ethicists, most clearly Jane Jacobs, see this as simple corruption. Nonetheless, corruption clearly has a cash value, involves some creativity to arrange, and is a decision factor. It is a skill like any other.
Perhaps because of this, not all theorists recognize individual capital as being as essential as labour, or distinct from social or political influence, or from instructional capacity. These theorists often refer to "intellectual capital", which more properly describes a debate or locus of complexity that arises when individuals take key instructional roles. Some refer to celebrity as another fusion, when individuals take key social roles.
Those who differentiate individual capital tend to see it as something that one can invest in, directly, and see grow, directly. For individual skill, even skill at a highly imitative enterprise, like sports or mastery of a musical instrument, this is very often quite measurable. Many enterprises, for instance, a music conservatory or circus school or creative writing coach, are clearly making a living on the identification and (somewhat) measurable enhancement of the individual.