Receiver Swaption equivalent to call option

I know I could just memorize that a receiver swaption is equivalent to call option, but I can’t rationalize it… Isn’t it true that in a receiver swaption the person receives fixed and pays float, so gain is to be made when interest rate drops. Doesn’t this seem more like a put option?

Are you sure you don’t mean a call option on the fixed income bond? (i.e. Not interest rate option, but on the price of the bond itself.)

It is like a call on a bond because when interest rates drop, you have already locked in the fixed payments at the higher rate. New swaps at expiration might offer a receive payment of 6% while you would receive 7%. So, a call on a bond at $100 for a coupon of 7% would be worth more if interest rates drop to 6%, as the price of the bond rises.