If you are shopping online for a griddle you better be specific in your query because griddles come in all sizes and shapes, and for all kinds of different uses. Just to prove the point - the best selling griddle on Amazon, the Calphalon 10 inch nonstick griddle, is actually a crepe pan. The short, gently sloping sides give it away. It is still a great buy as a nonstick griddle, especially when it's on sale for around as it is at the time of this writing.
Grill and Griddle
Let's sort out the difference between a grill and a griddle. A grill or grilling pan has a grid of raised ridges that prevent the food from cooking directly in the oil and drippings that accumulate in the bottom of the pan. If the range heat is pushed high enough you can get the same desirable grilling marks on steaks, chops and burgers that you see when you cook on outdoor charcoal and gas grills.
A griddle properly has a smooth, flat cooking surface, which makes it ideal for things like pancakes, omelets and crepes. A stove griddle, double griddle or double burner griddle (they all mean the same thing) are often reversible, with a flat griddle surface on one side and with grilling ridges on the reversible side. These griddles are often advertised as a reversible griddle or as a grill/griddle.
A reversible griddle is likely to be a 20 x 11 inch or so rectangle with short handles on each end. These griddles are called double burner griddles because they are big enough to cover and get heated by two stove burners at the same time. Coleman and Camp Chef make 24 inch and bigger griddles which are a bit large for a cooktop griddle but are ideally suited for outdoor use.
Round and Square
A round griddle is most likely a grill pan. A 10 inch or so smooth-bottom frying pan with sides just high enough to prevent oil and drippings from spilling over onto the burner, and with a conventional, long handle. The short sides are designed for easy spatula access to the food. You can appreciate that if you have tried to flip a pancake with an angled spatula. Since heat can be applied to only one side, round griddles are likely to have non stick surfaces.
A square griddle is also most likely a grill pan with short sides and a conventional handle. The advantage of the square shape is that it can fit more pieces. An 11 inch square griddle can fit four hamburgers or cheese sandwiches whereas three is the practical limit for a round griddle.
Steel, Aluminum, Stainless Steel and Cast Iron
Steel griddles are usually the larger rectangular kind, most are longer than 24 inches, and well suited for cooking for large groups. Nothing prevents you from using a steel griddle on your cooktop if it fits but most are made for camping stoves. The steel construction is rugged and can take some abuse from knives and metal cooking utensils.
Aluminum is less popular than it used to be but you can still find many sizes and shapes of aluminum griddles from top manufacturers, the Farberware Nonstick Double Burner Griddle among them. Thick aluminum is an excellent heat conductor although if not hard-anodized it can discolor and pit if cleaned with metal pads and harsh chemicals. Most aluminum griddles have at least one nonstick surface.
Variations of the cast iron griddle probably date back to the beginning of the iron age. Cooks who use cast iron cookware regularly have no problem maintaining the cookware to produce a nonstick cooking surface although newcomers still seem to get intimidated by the seasoning process. A cast iron griddle can be used indoors or out, dropped, and be thoroughly abused with utensils and searing cooking temperatures with no ill effect. Cast iron directly on charcoal is the only way the home cook can get the temperature high enough for a real blackened effect. Cast iron can be heavy so check the weight specs if you're a diminutive size.
Unexpectedly, a stainless steel griddle is rare. Even the stainless steel champion All-Clad makes only a hard-anodized aluminum griddle. There are a few models of 12 inch round stainless steel griddles but even these great cooking tools, from different manufacturers, for same strange reason have puny side handles that disqualify them from serious consideration.