I'm so confused with trig...
Why is the graph of sin(theta) different from the graph of sin(x)?
It isn't different, provided that $\displaystyle \theta$ and $\displaystyle x$ are measured in the same units. But if $\displaystyle \theta$ is measured in radians and $\displaystyle x$ is measured in degrees (say), then the scale of the horzontal axis will be different.
Another point "x" and "y" are typically used in a rectangular coordinate system and "r" and "$\displaystyle \theta$" are used in polar coordinates. You can, of course, use whatever letters you wish.
The graph of "y= sin(x)", in rectangular coordinates is the "sine wave".
The graph of "$\displaystyle r= sin(\theta)$", in polar coordinates is the circle with center at (0, 1/2) and radius 1/2, as $\displaystyle \theta$ goes from 0 to $\displaystyle \pi$.
But, again, the difference is because of the coordinate systems, not what the variables are called.