A visual (or perhaps optical) zoom is a real zoom on the camera lens that will reach out and give more real magnification of your subject like binoculars or a telescope. In your picture your subject will look larger and will have all the detail you'd expect it to have as if you were physically closer.
The digital zoom facility in a camera is a bit like enlarging and cropping a picture you already have; so magnification with a digital zoom effectively duplicates the dots that make it up horizontally and vertically. Sure your subject is bigger, but because the dots added are duplicates no extra detail is given. Indeed by enlarging by duplicating dots, or pixels, you might start to become more aware of lack of detail in your picture and it may start to look blurred or "blocky".
To get decent results in photographing wild birds requires either their cooperation in getting close to you, your determination to get close to them (which may require some form of hide to avoid scaring away timid birds), a lens with high magnification, or a combination of these.
On a budget the immediate options that strike me are :
1) v. cheap camera, scope and tripod (perhaps secondhand)
2) digital camcorder with large zoom
3) digital camera with long lens
Lots of questions spring to mind: would the photos just be intended as "records" rather than attractive photographs in their own right (maybe you've answered that one); are you interested in going down the digiscoping route with all the dedication and expense that could ultimately entail or is that a definite no no; do you already have the relevant computer hardware and software (perhaps quite demanding for option 2) which I know literally nothing about...)?
I'd imagine the more of these sorts of questions you can answer the better advice you'll get here from the experts on hand.
BTW, I'm a beginner and went with option 3) assuming that this really limited me to birds that would barely qualify as wild. Having said that, I've now seen results from forum members taken at 10-15x magnification which definitely ARE of wild birds. There's a thread about the camera I have at :
www.birdforum.net/forums/showthread.php?s=&threadid=5676
One of the posts contains links to the major digital camera review sites where you can get loadsa info on still digital cameras.
:t: