You use vectors in all of the above, I currently use Onyx, but I guarantee the plotter you are using is receiving vector data to make the cut. The graphic you are using is in rasters, forcing anything that plots your artwork to do a trace of the pixels to create vectors - not ideal, design in vectors/leave things in vectors (the rasterized type you are having trouble with did start life as vector art, but somewhere someone RIPed in to pixels, and now your software is tracing the pixels to try to recreate the vectors so you can plot it.... ever try to translate a phrase to and from another language? something is always lost in the translation - same thing here as your 2 trace engines are tracing different areas of the image.)
the type you are using is obviously pixelated - or raster graphics - if you keep everything as vectors, the software has a formulae to follow for the lines (and the plotter uses vectors to plot.) When you use rasters the software has to try to determine where a smooth line should go, but the only things defined are the pixels... and as you can see, different software can create different vectors from the same set of rasters. If you keep all artwork in vectors (or at least any edge artwork) then you will eliminate errors from different traces.
