pay for vs pay a school library card

[kwfine]

Happy New Year Alan!
I have just received a letter from my school librarian on the stroke of 00:00. He asked me if I had paid for a school library card.
Given that context, what is the difference between these two:
(1) You can pay for a library card via ABC Web. Vs (2) You can pay a library card via ABC Web.
I am confused of the 2nd sentence because I had heard some people say these:
"I forgot to pay for the gas bill","I forgot to pay the gas bill".
"Mum and Dad paid for my driving lessons", "Mum and Dad paid my driving lessons"

If it is wrong to say "pay for the card fee",
is it wrong to say "I have made the payment for the card fee" either?

Thank you.

Kitty

[Alan]

Happy New Year!

Pay FOR is correct, meaning 'buy with money'. However, you pay a bill (not pay for, since you do not buy the bill).