# Visualizing the difference curve in a 2D plot?

I have two functions $$f(x,y)$$ and $$g(x,y)$$. I wish to perform two tasks on a 2-dimensional figure:

1. Plot the curve where each point satisfies $$f(x,y)=g(x,y)$$.

2. Mark one side of the curve with red.

I tried to use Plot3D like the following

myfunc[x_, y_]:= If[f[x, y] < g(x, y), 1,0];
Plot3D[myfunc[x, y], {x, 0, 10}, {y, 0, 3}]


It gives what I expected, but how can I do this in a 2D plot?

RegionPlot[f[x, y] <= g[x, y], {x, 0, 10}, {y, 0, 3}]

ContourPlot[f[x, y] - g[x, y], {x, 0, 10}, {y, 0, 3},