The prefixes “macro” and “micro” are opposites, so it can be a bit confusing that in the context of photography, they refer to almost the same thing. “Macro” means big and “micro” means small, but in photography, they both refer to making small things look bigger. It is simply a matter of scale.
There are three related terms that exist along a spectrum: close-up photography, macro photography, and micro photography.
Close-up Photography

Close-up photography is exactly what it sounds like: photographs that show something close up, such that a small object fills the frame. Close-up shots can be taken with any camera, without the need for a special lens.
Macro Photography

Macro photography is extreme close-up photography that generally requires a special lens. An ordinary camera, whether it is a professional camera or a smartphone, cannot focus on a subject in extreme close-up without a macro lens. A common rule of thumb is that macro photography reproduces the subject on at least a 1:1 scale, so that the image is life size or larger.
Micro photography

Micro photography, which is also referred to as photomicrography, photomicroscopy, or microscopic photography, is at the extreme end of the spectrum, and involves capturing images of things that cannot be seen with the naked eye. Many of the techniques and products discussed on this site may be described as macro or micro, depending on the scale of magnification.