Aerosol and Particulate matter both are more or less similar with minor differences.
The aerosol is a colloidal suspension of solid particles or liquid particles in gases. They are finely divided particles.
Particulate matter is a heterogeneous discrete solid or liquid (single separate particle of Solid or Liquid). They are subdivided state.
To explain in a layman language aerosol can be liquid or solid particles in a gas. While referring any two (the liquid+gas or solid+gas) it would be called as aerosol while the concerned solid or liquid alone is referred as particulate matter.