A lens designed for photographing a close distance is called a macro lens.
In the macro lens, the magnification can be changed continuously, and the focal length is constant (unchanged) is called macro zoom lens.
Though the magnification can be changed continuously, the one whose focal length changes will not be strictly a zoom lens.
Sometimes it is called a variable magnification lens distinguished from a zoom lens.
If you do not change the magnification frequently and want to reduce the price, you should you variable magnification lens. If you change the magnification frequently, a macro zoom lens is recommended.