Types of microscope:
Stereo microscope : Binocular microscope
A binocular microscope refers to any microscope with two eyepieces
A binocular microscope refers to any microscope with two eyepieces. Compound or high power microscopes typically have two eyepieces which view images through a single high-power objective lens. The image presented to each eye is a flat, 2-dimentional 'mono' image. It is therefore also possible to have single eyepiece compound microscopes, which are typically very low cost systems used for educational purposes.
Stereo microscopes always have two eyepieces
Stereo microscopes always have two eyepieces, since stereoscopic vision requires two distinct images, one presented to the left eye, and one to the right. The result is a 3-dimentional 'stereo' image.
Summarising: A microscope with one eyepiece is always a compound microscope. A binocular microscope (a microscope with two eyepieces) could be a stereo microscope, or a compound microscope. However, a stereo microscope always has two eyepieces.
The exception: Stereo microscopes with no eyepieces!
But note, there is always an exception to the rule. Vision Engineering has a range of stereo microscopes which do not have any eyepieces, employing patented optical technology to replace the conventional eyepieces with a single viewing lens. Although these systems do not have eyepieces, the systems still have separate optical paths producing a true stereo microscope image.