Relation between Kleene star, union and difference in relation algebra
Consider $S=\{1,2,3\}$ and relations $A=\{(1,3)\}, B=\{(1,2)\}, C=\{(2,3)\}$. Then 

$A^*=(A\setminus B)^*= A\cup\{(i,i)\ |\ i\in S\}$,

$(B\cup C)^* = \{(i,j)\ |\ i,j\in S, i\le j\}$, and

$C^* = C\cup \{(i,i)|i\in S\}$.

In particular, $A^*\subseteq (B\cup C)^*$, but $(A\setminus B)^*\nsubseteq C^*$.