Are they the same or is there a difference?
I'd use "payday" in BrE, for the day employees get paid their wages.Or, in AE at least, "payday" as one word. I think that's more common than "pay day."
It would make no sense, since you are not my colleague. However, if someone from within the business who had to deal with suppliers were to ask me, I would understand what they meant immediately. However, I have no idea how widely the term is used, and whether other businesses use different terms. Payments to suppliers is not something I have have ever had any involvement with at other places I have worked.So if I asked you out of the blue ''when is our payment run?'' it would be understood right?!