Here is a side-by side of a single stack magazine (left) and a double-stack magazine (right):
Detail of the single-stack magazine
Note that the magazine body is slightly wider than the cartridges. Single-stack magazines generally feed slightly more reliably than double-stack magazines.
Detail of the double-stack magazine
Note that the magazine width is somewhat less than double the diameter of the cartridges. Not evident in the photo is the taper near the top of the magazine forcing the rounds into a single feed column.
Double-stack magazines have somewhat less than double the capacity of a magazine of similar length for the same caliber at the expense of slightly less reliability due to the chance of a jam caused by the taper to single-column feed.
Double-stack rifle magazines typically do not feature a single-column feed because rifles have the internal real estate for double feed ramps at the chamber mouth.
Handguns designed for double-stack magazines can technically accept single-stack magazines, which essentially waste magazine well space so the rounds feed single-stack. This is usually done to comply with magazine capacity limits in some states or for competition purposes.
A handgun designed for single-stack magazines is always a single-stack; it lacks the real estate in the magazine well to be anything but.