Quintessence and k-essence have been proposed as candidates for the dark
energy component of the universe that would be responsible of the currently
observed accelerated expansion. In this paper we investigate the degree of
resemblance between those two theoretical setups, and find that every
quintessence model can be viewed as a k-essence model generated by a kinetic
linear function. In addition, we show the true effects of k-essence begin at
second order in the expansion of the kinetic function in powers of the kinetic
energy.Comment: 14 pages, improved discussion, matches published versio