r1 = region[{{4, -3}, {-7, 6}}];
r2 = region[{{4, -7}, {0, 7}}];
RegionPlot[{r1, r2}, PlotRange -> {-10, 10}, BaseStyle -> 16, PlotLegends -> {r1, r2}]

r3 = RegionDifference[r1, r2];
RegionPlot[{r3}, PlotRange -> {-10, 10}, PlotLegends -> {r3}, BaseStyle -> 16]

r4 = RegionDifference[r2, r1];
RegionPlot[{r4}, PlotRange -> {-10, 10}, PlotLegends -> {r4}, BaseStyle -> 16]