We deal with two types of chaos: the well known chaos in the sense of Li and Yorke and $\omega$-chaos which was introduced in [S. Li, {\it Trans. Amer. Math. Soc.} 339 (1993)]. In this paper we prove that every bitransitive map $f \in C(I,I)$ is conjugate to $g \in C(I,I)$, which satisfies the following conditions, $1.$ there is a $c$-dense $\omega$-scrambled set for $g$, $2.$ there is an extremely LY-scrambled set for $g$ with full Lebesgue measure, $3.$ every $\omega$-scrambled set of $g$ has zero Lebesgue measure.