The cheaper, fixed-blade type is more commonly used in the modern construction trade.
With the advance of certain building methods and materials, designs specific to these trades have been developed.
One such modification being a sharpened point at the tip of the blade which can be pushed or jabbed through soft materials such as drywall without drilling a hole for the blade.
Compass saws typically feature a larger, coarser blade, and are designed to cut through tougher materials.
[1] Two power tools serving largely the same function but which work more quickly and with less effort are the jigsaw and spiral saw.