  In this article, the authors introduce the spaces of Lipschitz type on spaces
of homogeneous type in the sense of Coifman and Weiss, and discuss their
relations with Besov and Triebel-Lizorkin spaces. As an application, the
authors establish the difference characterization of Besov and Triebel-Lizorkin
spaces on spaces of homogeneous type. A major novelty of this article is that
all results presented in this article get rid of the dependence on the reverse
doubling assumption of the considered measure of the underlying space
${\mathcal X}$ via using the geometrical property of ${\mathcal X}$ expressed
by its dyadic reference points, dyadic cubes, and the (local) lower bound.
Moreover, some results when $p\le 1$ but near to $1$ are new even when
${\mathcal X}$ is an RD-space.
