Property is a generic term and it represents the general shown by all.
Characteristic is a specific term and it represents the individual.
If you say that
Matter is something which occupies space and has mass. This is a property of a matter.
Characteristic of matter means the individual property of solid, liquid or gas.
For ex.,
Solids
1. They have definite mass and has volume
2. The intermolecular force of attraction are high
3. Rate of diffusion is less.