Define topological conjugacy and $C^{1}$-conjugacy.

Let $a, b$ be real numbers with $a>b>0$ and let $F_{a}, F_{b}$ be the maps of $(0, \infty)$ to itself given by $F_{a}(x)=a x, F_{b}(x)=b x$. For which pairs $a, b$ are $F_{a}$ and $F_{b}$ topologically conjugate? Would the answer be the same for $C^{1}$-conjugacy? Justify your statements.