In practical terms, or just as an exercise in word origin? People fuss and fuss about how words change meaning or are used imprecisely in the food world, but the overlap here has been swirling for centuries. Our inclination would have been to say that cooking is the difference, but even in earlier times, that answer would have been misleading.
The derivation of both words and both dishes is French. Mousse means foam or froth. Souffle means breath, exhalation, puff, etc.
The term mousse has been used in France with regard to food at least since the middle of the 1700s. Most commonly it involves beaten egg white or whipped cream to achieve the desired foaminess. It may be stabilized with gelatin.
A savory mousse may include a puree of fish, poultry, ham, foie gras, vegetables, etc. It is most often put in a mold and cooked in a bain marie or water bath, although the meat or fish can be cooked in advance, without additional cooking once assembled. Such a mousse is generally served cold or lukewarm. A sweet mousse most often features fruit, chocolate, or coffee and is always cold.
A baked soufflé combines a sauce containing a roux, egg yolks, and a puree of sweet or savory flavoring ingredients, into which stiffly beaten egg whites are folded. The mixture is baked in the oven, and rises through expansion of the air bubbles in the egg white.
Savory soufflés can include fish and shellfish, poultry (white meat or livers) and game birds, ham, offal, cheese, vegetables, etc. A dessert soufflé can be based on either a roux or a pastry cream, bound with egg yolks, and including some flavoring (fruit, liqueur, vanilla, chocolate, etc.)
Generally a soufflé is baked in a round soufflé dish, to which a paper collar has been added so that the soufflé is held in place as it rises and doesn't drip down the sides of the dish. Technically this is not necessary, as a well-folded soufflé made with stiff whites will rise in place as it bakes. Soufflés may also be baked in individual ramekins.
Now a cold or iced soufflé, which has existed for at least 250 years, is one of the great jokes of the kitchen. The mixture, which may include ice cream, whipped cream, sponge cake, fruit in syrup, candied fruit, or a fruit puree, in layers or mixed together, may be poured into a soufflé mold which has also been extended with a paper collar. It may be frozen, or if only chilled, firmed up with the addition of gelatin. When presented, the paper is removed, revealing a dessert rising above the sides of the mold, resembling a baked soufflé.
Might that not be a mousse? Answer: it is whatever its maker calls it.
A baked soufflé does its rising in the oven. A mousse doesn't really rise once it has been assembled, even though it may be gently cooked. It may not be possible to distinguish between a cold soufflé and a mousse, but if it is obvious that your host has put lots of effort into making a cold dessert that looks an awful lot like a soufflé, do everyone a favor and gush over his wonderful soufflé….