Simply said, a shadow box picture frame has at least one raised window mat that will cast a shadow on the artwork whereas a 
hasn't. In the example photo shown here the light blue mat is raised and casts a shadow over the child's artwork underneath. And while there are other matting and spacing variations, this is the main variation between the two styles. Again referring to the self-same illustration, many shadow box frames have one or more mats recessed at the bottom of the frame so that the shadow is cast still, but lower.
In fact, these special picture frames are a hybrid of box frame and shadow box frame. Certainly this type of specialized picture frame has evolved from the days when shadow boxes were almost exclusively made to hold and display antiquaria, numismatica or militaria.
Nowadays, many shadow box creations are crafted by individuals rather than picture framers. Craft-persons, home makers and home decor enthusiasts quite imaginatively and cleverly craft, build and stitch all manners and kind of objects inside the frame. A box frame, on the hand, usually doesn't have mat. In this other illustration shown below, there is no shadow created by the mat because there is no mat:
The box frame is so called because, unlike most picture frame or photo frame mouldings, the side of the frame is larger, wider or bigger than the top. Essentially, the box frame is a shadow box frame without matting. In the pine, wood box frame above the fitted glass is raised and above the face paper where the artwork would be mounted. The glass pane rests on strips of wood although it ca just as easily rest on white or black foamboard.
With both a shadow box frame and box frame, a large variety of 3-dimensional items and object may be mounted within. The height of the moulding (the frame) will determine how tall or big an object may be framed. When you have a variety of, or a particular difficult or delicate or valuable item to be mounted or framed, a specialist picture framer who specializes in object framing may be best suited to do the work. Naturally a specialist picture framer will charge for his or her work. If you prefer not to pay a framer for this work and do it yourself, you probably can.
Many hardware stores and craft stores sell different shadow boxes in different sizes. These tend to be fairly inexpensive and are often raw, or unpainted, so that you can paint or spray them whatever colour you want. Depending from where you source you shadow box frame, it may also come with inserts or mats so that you can craft a multi-shadow box with multiple depths and levels.
Bought some shadow box frames online from a top US frame store and these were much better that the picture frames you can get here from Ikea or Officeworks. The US ones have several mats, come in more colours and finishes, have a better, more quality finish and all have stands so that you can stand them or hang them. The shipping to Australia was only $35 and for me it was worth it.
Shadow Box allows you to protect, preserve, and display 3D objects too while simple box frame misses this advantage. Most importantly it uses matting.When used in a frame, the mat keeps the photograph from touching and adhering to the frame’s glass. Another advantage of the window mat is that in case a photograph is handled frequently, as with a portfolio for private viewing viewers touch the mat rather than the photograph.
Thanks! The explanation you’ve provided is pretty concise yet explanatory. So in a nutshell, the basic difference is that shadow box frames have window mats or have matting (under which there are spacers which raise the height from the backing board and thence cast a shadow ) whereas a simple box frame doesn’t.