Changing the mode in the calculator changes the scaling of the x-axis. If you are in radian mode and graph the curve, then you get one arch of the sine curve on \[0,π\]. If you do it in degrees, then that same arch is stretched over \[0,180\]. In both of these cases, the maximum value of the curve is 1.
Now forget about the sine curve for a minute and imagine doing this with a rectangle. Your height is always 1, but the width is changing from \~3.14 to 180. Naturally, the numeric value of the area is going to change.
This is similar to changing your width units from feet to inches. If you draw a rectangle that is 1 foot wide, then the numeric value of that area is going to be 1/12th of what you'd get if you think of that rectangle as 12 inches wide. But it's the same rectangle.