There is abundance of literature regarding startup financing, rationale for public support etc. but I cannot find any source that explicite provide 'startup' definition.
there is no secret in this term, it is a new enterprise. It is used both to a new company in an already open economic sector and in a completely new market - as Uber, e. g..
From this concept, various theories developed different models of the firm.
I really don’t know how new the term is, but I guess it strengthened itself in the end of the 1990s, when Nasdaq and all the dot.com companies gained relevance. How bit is another hard question, but I might say this term is largely used, in several disciplines of science, such as economics, finance, accounting, business management, and so forth.