Is a LU card the same thing as a student card?

No, your LU card and your student card are two different things.

Your LU card is your university ID card. It also serves as a print & copy card, library card and access pass. It remains valid for the duration of your studies. You need to request a LU card yourself. You will not receive it automatically. 

Your student card is proof that you are registered as a student of Leiden University. It is valid for a maximum of one academic year. You will receive it automatically after you complete student (re)registration formalities each academic year.