I want to smooth the lines without blurring the patterns on the mesh

Hello, I am a beginner with Rhino. I’m not originally an expert in Rhino, but since no one else could handle it, I ended up taking on the task. We are working on a project at the company, and the original file was created in 3D Max. When I imported it into Rhino, it appeared as a mesh of triangular polygons. Another company managed to create a smooth output, but I had no idea how to achieve that, so I just handed it over to them. However, I want to do a better job next time, so I have a question.

The first picture is a file I worked on after importing the .obj file from 3D Max into Rhino. The second picture is the work done by the other person. In the CNC CAM, my work showed up with lines that were too jagged and uneven, making it unusable. How can I work in Rhino to achieve results like the other person’s?

Additionally, the mesh surface has patterns, but when I smooth it, these patterns get blurred, which is problematic. The other person managed to keep these patterns while making it smooth. How can I achieve that in Rhino?

No pictures attached.