A normal single-cylinder crankshaft has two bearings that support it - one on each end. In between it has an offset bearing ('crankpin') that supports the connecting rod. The loads transferred to the crankshaft by the connecting rod are resisted by a crankshaft bearing on each side of the crankpin - the 'main bearings' at the two opposite ends of the crankshaft. An el cheapo engine, not intended to last very long, may leave out the second half of the crankshaft: in effect, by sawing it off at one side of the crankpin. This does not support the crankpin very well, and results in the crankshaft vibrating and whipping about.
With good design, the result of leaving out half of the crankshaft can be a quite satisfactory operating life and a considerably cheaper engine. If a reputable manufacturer like B&S can run an aluminium piston directly in an aluminium cylinder bore - which metallurgy tells you is a no-no because aluminium loves to seize onto other pieces of aluminium - then why not commit other engineering atrocities as well? How long do people expect a lawnmower to last anyway, and how many owners do something awful to it themselves, such as leaving the oil out of the fuel of a 2-stroke, or failing to keep oil in the sump of a 4-stroke?
The answer to your actual question is that a full-crank is simply a normal crankshaft, such as you will find in just about any engine intended to last more than a few hours. A half-crank, or cantilevered crank, is a single-main-bearing crankshaft - the mere contemplation of which makes some of us retch.
