Not all lenses are "macro" lenses. A lens can have a "macro" setting to allow the user to get very close to a subject. However, one can use a lens without the macro setting to take such photos.
There are close-up filters one can attach to any lens, but these filters could be as expensive as some macro lenses depending on the level of quality. I have some cheap close-up filters I purchased trying to save some money, but they are pretty much useless. A good quality Hoya close-up filter could cost from $200.00 to $400.00.
There are some lenses without a macro settings you can use for macro photography. For example, Canon's 50 mm f/1.8. Just attach a Kenko tube to the camera, and mount the lens on the Kenko tube. This will allow you to get as close as a few millimeters for a lady bug or something like that. The kenko tubes are sold in a set of three tubes, and cost around $160.00 at B&H and some other camera stores. The "nifty 50" (lens above) costs around $80.00 (as far as I remember).
A macro lens such as a Sigma 105 mm one allows you to get just as close to the subject, and without having to use a close-up filter or a Kenko tube. It also allows you to close the distance (twice) to a far subject over the 50 mm lens. However, for taking pictures of people near you, the 50 mm gives you a wider field of view than the 105 mm one.
A zoom such as the "kit" lens (17-55 mm) allows you for a much wider field of view at 17 mm. For example, when taking pictures of your family indoors. In this case you may at times be not able to use the lens at 50 mm if you want to show their whole bodies from head to toe, but set at 17 mm may sometimes allow you to do so.
Take a look at this photo. I set the kit lens at 17 mm to attain a wide view. The trees and other parts of the subject look far away, and small:
This one was taken with a Tamron 17-50 mm lens, set at 50 mm. As you can see, the subject looks much closer or larger:
I took this one with a Sigma 70-300 mm lens that has a macro setting. The lens was set at 300 mm, because that's how the macro switch works with this lens. Notice how subject takes most of the picture. This is a close-up: