For partial recurrence equations, RSolve generates arbitrary functions C[n][...].
Solutions given by RSolve sometimes include sums that cannot be carried out explicitly by Sum. Dummy variables with local names are used in such sums.
RSolve sometimes gives implicit solutions in terms of Solve.
RSolve handles both ordinary difference equations and q-difference equations.
RSolve handles difference-algebraic equations as well as ordinary difference equations.
RSolve can solve linear recurrence equations of any order with constant coefficients. It can also solve many linear equations up to second order with non-constant coefficients, as well as many nonlinear equations.