ppls

As I understand now payer swaption = put on BONDS.

PUT on bonds - you want bond value to fall for the put to be in the money. Bond values fall when rates go UP. You want rates to go UP to "win".

Payer Swaption - pay fixed rate is the strike (set at initiation), so you want rates to rise over strike meaning you are paying this fixed amount that is lower than the fixed amount that fools in the market have to pay.

In both cases you WIN if rates go UP.

Flip it and you can see why receiver swaption = call on BONDS.