Sorry yes got them backwards. The BN is from the federal governement and is only needed by business that import, export or collect GST/HST.

The BIN is from theOntario provincial government and used only when communicating with the Ontario government which is why Revenue Canada will tell you that they won't accept it and want the SIN on the receipts. There have been conflicting reports on that too as to whether we have to include it or not or if parents can claim without.