Wide-angle Lens:
 A lens that has a shorter focal length and a wider field of view (includes more subject area) than a normal lens.
Zoom Lens:
 A lens in which you adjust the focal length over a wide range. In effect, this gives you lenses of many focal lengths.
Telephoto Lens: A lens that makes a subject appear larger on film than does a normal lens at the same camera-to-subject distance. A telephoto lens has a longer focal length and narrower field of view than a normal lens. -KODAK: A Glossary of Photographic Terms

Most consumer-grade digital cameras offer optical and digital zoom.
Ignore the digital zoom.
Your photos will be at their sharpest with the optical zoom, turn off the digital zoom. Why?

Optical zoom uses the optics of the lens of the camera to bring the subject closer. Digital zoom is an invention that enlarges that image within the camera.
Optical zoom
is what the lens actually sees. This is what matters most.
-optical zoom is a true zoom.
It's focal length actually extends and retracts. An image is magnified by the lens itself.
-An optical zoom produces quality images.
-A zoom lens is used to magnify an image 3X, 4X, 10X and more.
-If you want to zoom in close to distant objects, buy a camera with the longest zoom you can afford.
-NOTE: Very long zooms are prone to camera shake, particularly in low light. To help prevent this, some digital cameras have image stabilization.
Digital zoom uses in-camera technology to enlarge the pixels in the image the optical zoom captures, then enlarges them. The result is poor; loss of sharpness, color, and image detail.
A digital zoom is not a true zoom.
-It is a simulated zoom that enlarges the central portion of an image.
-The actual length of the lens does not change.
-A digital zoom pre-crops the center area of an image. Resolution is reduced, giving the appearance of zooming in.
-It is similar to cropping with photo editing software.
-A digital camera may have an option to turn off the digital zoom.TURN IT OFF!

Optical Zoom vs. 35mm lens
-Expressing focal lengths in terms of 35mm equivalent makes it easier for individuals to understand so they can compare digital camera lenses.
-The focal length is the same on all 35mm cameras because the size of the film each uses is the same.
-Digital cameras, however, have different focal lengths because the size of their image sensors vary from one camera to another.
-3x optical zoom on one digital camera may not give the same magnification as another with a 3x zoom.
EXAMPLE: The Nikon 5400 has a 4x zoom, which has a 116mm equivalent focal length. But Nikon 5200, which has a 3x zoom, has a 115mm equivalent focal length.
-Not much difference yet one is a 3x and the other is 4x. This is why it's important to ask the 35mm equivalent when looking for a specific focal length.

Digital cameras have different methods of focusing, so check the manual.

When using an automatic mode, focus is locked when the shutter-release button is pressed half-way down. Correct use of the two-step shutter button is key to obtaining proper focus.

The LCD or electronic viewfinder indicates when, and sometimes where, focus is locked.
Usually there is a visual indicator, such as a small lamp or change in color of the focus indicator, that confirms when focus is achieved.

Focus is fixed until you press the focus button again or switch to a different focus mode.