Why does the Ubuntu Budgie desktop look different, compared to the Solus version?

Short answer is guess is because the devs have selected a different default appearance.

If you open Budgie Welcome, Themes and Layouts, you can look through the different desktop layouts. Just be warned if you apply a new layout, you will have to add back any custom changes you made to the Budgie panel.

But if you apply both the Plata makeover and the Traditional Budgie layout, you will get it to look like the Solus default.

This not my preferred layout, I like the top bar. But, yeah, if you change a few settings, this is also Ubuntu Budgie: