If an engine is not being fed any fuel and the crankshaft is not rotating, is it running? Of course not. But would you say it is stopped or paused? Both, it makes no difference. It's simply a semantic distinction with no difference in real meaning. Mazda has introduced a new kind of automatic start-stop system on the 2010 Mazda3 called i-Stop. Until now, such systems primarily consisted of using either a beefed up starter motor or an alternator integrated with starter motor functionality to restart the engine. These units have to be more robust in order to withstand the greater number of engine start cycles that are required compared to traditional engines.
Mazda's system takes advantage of direct injection and a crank position sensor to re-start the engine without a stronger starter. The engine is stopped/paused with one of the pistons in the middle of its power stroke. During re-start, fuel is sprayed directly into the cylinder and then ignited. The force of the expanding and combusting fuel pushes the piston down, taking the load off the starter. Thus, the engine can re-start more quickly and smoothly.
Gizmag calls this pausing the engine rather than stopping it, but Mazda never uses that term in any of its press materials. Currently the i-Stop system is not available on the U.S. market 3, but it will likely arrive eventually.