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