払う and 支払う

Is there a difference between 払う and 支払う, it seems to have the very same meaning.

The latter has a more narrow use. It all depends on context.

Yeah, just accept and get used to it.

There are so many pairs like that which seem to have the same meaning, only one slightly more specific or more extreme or with some other degree of difference.

In this case, though it's more straightforward since we can say 支払い is closer to an act of payment, or making a payment (on debt, credit, bills) whereas 払う can be thought of as simply to pay (money, attention, respect....).