Circulation around a curve

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in a previous question I had asked

How to apply the divergence thereom in the plane

About the divergence of $F=(xy)i+(2x-y)j$ where C is the triangle with verticies $(0,0)$ , $(1,0)$ and $(0,1)$.

I did this and solved for $\frac{-1}{3}$

My question is now;

Is this$\frac{-1}{3}$ also the circulation of $F$ around $C?$ The reason I ask is because I find myself a bit confused with what circulation is. It seems like it is obtained by taking the line integral over C, which is why it seems to me the answer would be the same. To get a better understanding and such say F= velocity=v

is the integral $\int_{C} v \bullet n ds$ the angular velocity of a fluid, and $\int_{C} v \bullet dR$ the angular speed? Arent they same?

Im just feeling confused about this. Hopefully someone can help to clear this up.

Thank you