Fireworks works with both vector based objects and bitmap. There are two workflows open to you:
1) right-mouse click the rectangle layer, and choose "flatten selection". The vector layer is then converted to a bitmap layer. Next, use the bitmap selection tool (M), and create your selection. Then use the pointer tool (V) to move the content.
2) generally you want to keep the vector objects if you can. Working with vector graphics is entirely different compared to bitmaps, and the rules and tools change. To recreate your effect, you must draw a second rectangle, place it partly over the original rectangle, and then select both. Then open the Path palette (in the Window menu), and click on the first button under "combine paths'.
Fireworks is on a completely different level compared to Paint. If you have never worked with these type of more professional applications, I urge you to watch a couple of video tutorials.
Do realize, though, that Fireworks is EOL software: it's dead in the water. Adobe stopped development last year. You may want to invest your time in other software.