Interesting, I always thought the R4s were based on the R1 which was based on the FN from Belgium.
R1s and R4s are completely different rifles. You are correct that the R1 is the Belgium FN (don't think there is any actual difference just we gave it our own designation) which is chambered for 7.62mm NATO. The R4 however is based an the Israeli Galil which in turn was based on the AK-47 and is chambered for 5.56mm NATO ammunition. If you look carefully at the R4 and an AK you will notice the similarity.