It can be tough to find an answer to the satchel vs. messenger bag question because really, a messenger bag is a type of satchel. Satchels come in a multitude of shapes and sizes, in a variety of materials, with all types of straps and handles.
But, there are three key features of a satchel that qualify it as a messenger bag:
Messenger bags have a cross-body strap and are meant to be worn against the lower back, then pulled around to the side or front to access the contents. This makes them ideal for wearing while walking or riding a bike (a nod to their history of use by bike couriers).
Messenger bags originated with couriers (or messengers - hence the clever name) delivering important documents; so, a true messenger bag will have a means of closing securely in order to protect its contents. Buckles, clasps, and zippers are commonly used and can easily add as much style to a messenger bag as function.
Messenger bags tend to be associated with briefcases and are therefore seen as a bit more formal (than, say, a backpack). A messenger bag can also, of course, be used casually, but if you plan to use the bag in a more formal setting like a business meeting, it will get the job done. Traditionally, a messenger bag will have a weather-proof exterior such as waxed canvas (which would’ve been crucial for a bike courier back in the day), but messenger bags can now also be found in leather, which adds to the professional briefcase bag style.