What is the difference between aerosol and foam?

Hint: Aerosol and foam both are colloidal systems. A colloidal state is a state between true solution and suspension state.

Complete step by step answer:
First of all let us understand about colloidal systems. A colonial system is retrogenes in nature consisting of two phases; dispersed phase and dispersion medium. The colonial particles constitute the dispersed phase and are just life solute in a true solution. The medium in which the colloidal particle is scattered is the dispersion medium. Thus, a colloid is a heterogeneous system in which one substance is dispersed as very tiny particles in another substance called dispersion medium. Collides have properties intermediate between true solution and suspension. Colloids are generally translucent solutions. With particle size between 1nm. And 100nm. The particles of colloids can pass through ordinary filter paper but not through animal membrane and they don't settle under the centrifugation. Moreover the particles are not visible to naked eye but can be seen under ultramicroscopic.
Aerosol and foam both are the type of colloidal system. An aerosol is a suspension of fine solid. Particles or liquids in air or another or another gas. Depending on dispersed phase, aerosols are of two types.
(i) Aerosol of solid- In this system dispersed phase is solid and dispersion medium is gas. Some examples are- smoke, dust etc.
(ii) Aerosol of liquid- In this colloidal system, dispersed phase is liquid and dispersion is gas. E.g. Mist, cloud etc.
Foam is an object formed by trapping pockets of gas in liquid or solid. It is also of 2 types.
(i) Liquid foam- it is a colloidal system in which dispersed phase is gas and dispersion medium is liquid e.g. Soap leather, whipped glam etc.
(ii) Solid foam; It is a colloidal system in which the dispersed phase is gas and dispersion medium is solid. Eg. Pumice. Stone, styrene foam. Foam rubber etc.

Note:
In Aerosol, dispersion medium is always gas dispersed phase can be solid or liquid whereas in foam, dispersed phase Is always gas and dispersion medium can be solid or liquid.