The terms soft and stiff peak are associated with whisking cream and egg whites. When cream is whipped, air is knocked into the fat molecules. The more you whip, the more air goes in until eventually the fat molecules are saturated with air and the liquid content of the cream is squeezed out.
When a recipe requires semi-whipped or softly whipped cream, it should just hold its own weight in the bowl, especially when further mixing is required, as when making a mousse.
Sponge and other cakes normally require egg whites to be whisked to a soft peak while meringue or soufflés require a stiff peak. As the sponge has other aerating properties, too much rise from the eggs will give an over-aerated product with very little structure once removed from the oven.