What's the difference between a 'shower' and an 'outbreak of rain'?

In fact, if you are caught out in one, there is no difference. You can still get wet! Meteorologists however distinguish between precipitation (rain, snow, hail etc.) falling from cumuliform cloud in an unstable environment - a shower, from that falling from layer clouds in a generally stable environment which are just called rain, snow, sleet etc.

However, rain from layer cloud in a frontal situation for example can be rather hit-and-miss, especially in a weakening situation, and so forecasters will try and get around such problems by talking about 'patchy rain', 'outbreaks of rain', 'splashes of rain' etc. The opposite problem comes when a well defined trough sweeps across an area, in which the cloud structure is most likely of an unstable type: cumulus, cumulonimbus and altocumulus.

Given the definition above, the short, very sharp falls of rain might be called 'showers' (and probably coded as such by observers), but this would be misleading to members of the public caught out in such precipitation: hence the 'showery outbreaks of rain', 'showery bursts of rain', 'localised downpours' etc.