Let us consider the operator-theoretic difference of two composition operators acting on a weighted Hilbert Bergman space. In 2011, Choe , Hosokawa and Koo [CHK] proved a necessary and sufficient condition under which the difference operator is Hilbert-Schmidt. In this dissertation, we have provided a simpler proof of their result , using a change of variable method. Applying that method, we have also established similar necessary and sufficient integral condition under which a difference operator of a more general form is Hilbert-Schmidt. In 2011, Saukko [S] found a beautiful way of characterizing the boundedness and compactness of the difference of two composition operators , acting in between two weighted Bergman spaces. More precisely, he was able to reduce those problems for a difference operator into corresponding problems for a weighted composition operator, which were already solved in the year 2007. In this work, we have generalized Saukko's results for the same operator where the target function space is more general. Through these generalized results, we have been able to characterize the boundedness and compactness of the previously mentioned difference operator with a more general form.