For the Bird photos you would need a good Telephoto lens. For the Flowers you would need a good Macro lens. In most cases these are two very different type of lenses. Compact cameras achieves this by using digital zoom. That will not give you the best quality photo due to Artifacting and Stair Stepping (Jagged, rough or step-like reproduction of a line or boundary that is originally smooth).
A D-SLR would be best because of interchangeable lenses. This way there wold be no digital zoom to affect the image. Yes...D-SLR cameras are more heavy, but this helps give a more stable image in most cases because you use your muscles differently with the extra weight.
However, both the Bird and Flower Photography would be best done with a tripod. The extreme Zoom for the Bird photos make shaking of the camera an issue and the longer exposure of the Flower photos make vibration blur occur.
Image Stabilization is available in Body and Lenses. Sony Alpha D-SLR cameras have it built into the body so any lens you put on is stabilized. Canon has a line of IS (Image Stabilized)lenses as does Nikon in the VR(Vibration Reduction) Line.