Floating rate bond valuation

Hi, I would like to know how a floating rate bond will be valued when LIBOR is used to compute the coupon cashflows and the bond is discounted using an OIS rate. Normally I have seen valuation of a FRB when both the coupon and discount curves are the same. What happens when these are different?

What you have seen is right. The other is hypothetical and does not quite any meaning to the concept of FRN