The two visualizations are very different. What you segmented is a surface rendering of a surface model created from a labelmap of the segmentation. The image you pasted from the DICOM viewer is a volume rendering, which is a visualization technique directly from the volume. Read a bit on this here:
The segmentation is mostly based on intensities, and is usually not perfect. Also the output of it is a binary mask volume (i.e. labelmap), which is by definition “not smooth”. You can do further smoothing in Segment Editor using the Smoothing effect, or you can increase the smoothing factor applied for the surface conversion under the small arrow next to the Show 3D button.