The 55-200mm is an "optical zoom".
There are two versions of the Nikkor 55-200mm lens.
AF-S DX Zoom-Nikkor 55-200mm f4-5.6G ED.
This lens does not have Nikon's "Vibration Reduction" (VR) and does not have "Internal Focusing" (IF). VR is good to have when shooting at slower shutter speeds like 1/60 or 1/30 sec. Using a polarizer filter is more difficult when a lens doesn't have IF because the front element rotates as you focus. $229.95 @ B&H.
AF-S DX VR Zoom-Nikkor 55-200mm f4-5.6G IF-ED.
This lens has Nikon's VR and is an IF lens. It would be the better choice of the two. $589.95 @ B&H.
Both lenses are designed for the "cropped sensor" of your D60. They can be used on a full-frame sensor DSLR like the Nikon D700, D3 and D3x but the image will be the same size as it is on your D60.
Both lenses have a variable aperture which means when you're shooting "wide open" (f4 @ 55mm) and zoom to 200mm (f5.6) you lose a full stop and your shutter speed will decrease. If your shutter speed at 55mm @ f4 is 1/100 sec. and you zoom to 200mm @ f5.6 your shutter speed will be 1/50 sec. This is why you'll want the VR.
In my opinion, if you have the money, the AF-S Zoom-Nikkor 70-200mm f2.8G VR II IF ED lens would be far superior to either of the 55-200mm lenses. Since its not a "DX" lens you can use it on a D700 or D3 or D3x and get the full benefit of the full-frame sensor. More importantly, its a full stop faster at 70mm than the 55mm (f2.8 vs f4) and two full stops faster at 200mm (f2.8 vs f5.6). So if your shutter speed with the 55-200mm lens is 1/100 sec. at f4, your shutter speed at 70mm at f2.8 will be 1/200 sec. - and it will be 1/200 sec. when you zoom to 200mm. $1,899.95 @ B&H.
B&H - http://www.bhphotovideo.com
If the 70-200mm f2.8 is out of your budget, then choose the 55-200mm f4-5.6G VR IF-ED lens.
There is no such thing as "digital zoom" on a DSLR. With an editing program you can crop and enlarge a section of your image file but that isn't anything like the "digital zoom" of a compact digicam.