Macro photography:
It refers to close-up photography; the classical definition that the image projected on the "film plane" (i.e film or a digital sensor) is close to the same size as the subject. On 35 mm film (for example), the lens is typically optimized to focus sharply on a small area approaching the size of the film frame. Most 35mm format macro lenses achieve at least 1:2, that is to say, the image on the film is 1/2 the size of the object being photographed. Many 35mm macro lenses are 1:1, meaning the image on the film is the same size as the object being photographed. Another important distinction is that lenses designed for macro are usually at their sharpest at macro focus distances and are not quite as sharp at other focus distances.
In recent years, the term macro has been used in marketing material to mean being able to focus on a subject close enough so that when a regular 4×6 inch (102×152 mm) print is made, the image is life-size or larger. This requires a magnification ratio of only approximately 1:4, more easily attainable by lens makers.
Digital zoom:
Digital zoom is a method of decreasing (narrowing) the apparent angle of view of a digital photographic or video image. Digital zoom is accomplished by cropping an image down to a centered area with the same aspect ratio as the original, and usually also interpolating the result back up to the pixel dimensions of the original. It is accomplished electronically, without any adjustment of the camera's optics, and no optical resolution is gained in the process.
Because interpolation disturbs the original pixel layout of the image, as captured by the camera's image sensor, it is usually considered detrimental to image quality. The results of digital zoom are, however, sometimes superior to the results of manual cropping and resizing (interpolation) in post-production. This is because the camera may apply its interpolation before performing lossy image compression, thereby preserving small details that would otherwise be lost. For cameras that save images in a raw format, however, resizing in post-production will yield results equal or superior to digital zoom.