Sabam and the Fair Remuneration work completely independently of each other and represent other types of rights.
Sabam represents the rights of authors, composers and publishers (copyrights). The Fair Remuneration represents the rights of performing artists and record producers (neighbouring rights).
If you play pre-recorded music in a public space (e.g. CDs, records, etc.), you will have to pay both Sabam and the Fair Remuneration.
If the music is live, you only need to request a licence from Sabam.
You can find more information about the Fair Remuneration on their website.