I do most of my graphing using Desmos, and also use graphing as a visual check for some of the math that I'm a little more wary of when I don't have access to someone to double check my work. I was doing something when I noticed a discrepancy which boils down to the title question. Above is a picture of Desmos's graph of those two equations. If it's just a problem with the calculator, I'll soon report it as a bug and be very relived that math isn't broken.
The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=\sin(9\theta)$ and $y=0.77\sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.