Dissecting microscopes are stereo microscopes. Key characteristics is that they give a stereo view* and have sufficient space between the objective (bottom lens) and the subject when focussed to allow you to get your hands in and manipulate. Manipulation of the subject generally takes place under the microscope, e.g. dissection, and the stereo view gives necessary depth perception. Useful magnifications of x10 - x30 for beekeepers.
Compound microscopes may have 1,2,3 or indeed 4 eyepieces, but still have one set of optics, so cannot give a stereo view. Objective lenses are usually on a turret - used to rotate different magnification objectives into usage. Very short distance (~ 1mm) between the objective lens and the subject, which precludes any manipulation with tools. Subjects are generally manipulated elsewhere, mounted on a glass slide, then look at under the compound microscope. Useful magnifications of x40 - x400 for beekeepers, x1000 if you want to look at foul brood specimens.
Bob Maurer's new book
Practical Microscopy for Beekeepers - launched at the National Honey Show - is excellent. It will take you from the above descriptions being gobbledeygook to being able to make up pollen slides, perform dissections, do nosema diagnosis, etc. Money well spent at £15.
Remember also the "buy cheap, buy twice" mantra when looking at the £50 - £100 microscopes. Do not believe the claims for magnification, because whilst they can make blobs look big they cannot make big blobs look detailed at that price. Detail is what you need and is what people pay for in optics
£150 - £300 buys some damn good microscopes these days.
ETA: you can get various eyepiece mounts for digital cameras to allow you to take photos down either type of microscope with your existing camera (generally). Then there are dedicated cameras available and again price is open-ended.
*Two eyepieces does not mean stereo view. Stereo comes from the microscope being designed with a set of lenses for each eyepiece. The image inversion is corrected using prisms so that you see the subject the right way up. Both these features are present in stereo microscopes and absent in compound microscopes.
