Hi,
It is the same thing. In both cases those "fourragères" were provided by military tailors or private companies.
Usually, they used to have a special engraved "ferret" and often a double suplementary lanyard over the shoulder, like for the "fourragère double".
This was a fashion which started in the 20s.
Nowadays, it is very rare to see that kind of "fourragère fantoche" worn in uniform.
Regards
Bison