Flush cutters and side cutters are tools frequently used in jewelry making for cutting wire. The terms are not always used precisely but a direct comparison is usually not appropriate. Generally, “side cutter” refers to a type of pliers, and “flush cutter” is a member of a narrower category -- a type of side cutter.
Pliers
Both of these types are variations of basic hand tools called pliers, or diagonal pliers. These tools are a type of lever, with two arms hinged at a fulcrum. As the user squeezes the tool’s handles, the opposite ends of the tool close -- gripping, crushing or cutting an object between them.
Side Cutters
Side cutters are pliers with two beveled edges on the ends. As the handles are closed, these edges align exactly, pinching or wedging through the object between them. This is a different action than produced by scissors, for example, which shear objects -- the blades passing by one another. The flat, or flush, side of the cutting end of the pliers is typically located to one side, hence the name of the tool. Side cutters come in a wide variety of sizes but those used in jewelry making are typically small to allow precise use.
Flush Cutters
Flush cutters are so named because they are intended to snip the end of a thin piece of jewelry wire, leaving it even, or flush. They range in size and design but all share the same intent -- to provide the jeweler with a smooth surface on the wire so it can then be shaped or soldered. Other types of cutters may leave an angled or ragged end on the wire that has been cut. To accomplish a smooth cut, flush cutters have finer, sharper edges that help them avoid leaving a ridge on the wire, sometimes called a pinch.
Considerations
Because their ability to cut cleanly depends on the sharpness of their edges, flush cutters are designed by their manufacturers for a specific thickness of wire. Exceeding their recommended range risks denting the cutting edges and significantly impairing their performance. For example, using a very small pair of flush cutters on a thick piece of wire will not only damage the cutters, but leave a noticeable pinch on the wire. The hardness of the wire must also be considered. Notably, memory wire is quite hard and manufacturers specifically produce memory wire cutters to handle it.