  We build on the formalism developed in [arXiv:1906.08372v1] to propose new
representations of solutions to Stein equations. We provide new uniform and non
uniform bounds on these solutions (a.k.a.\ Stein factors). We use these
representations to obtain representations for differences between expectations
in terms of solutions to the Stein equations. We apply these to compute
abstract Stein-type bounds on Kolmogorov, Total Variation and Wasserstein
distances between arbitrary distributions. We apply our results to several
illustrative examples, and compare our results with current literature on the
same topic, whenever possible. In all occurrences our results are competitive.
