HAVE and HAVE GOT mean the same, but their grammar is different.

I have a bike = I've got a bike
I don't have a bike = I haven't got a bike
Do you have a bike = Have you got a bike?

HAVE is more used in American English. HAVE GOT is more used in British English, but in formal English or writing, British people also prefer HAVE.

Americans do use the verb HAVE GOT a lot, but they drop the HAVE, so they only use GOT:

(BrE) I've got a bike = (AmE) I got a bike

But in the negative, Americans use "I don't have a bike", or the very colloquial form "I AIN'T got a bike". For questions they always say "do you have...?"

IN THE PAST

I have a book --> I had a book
I don't have a book --> I didn't have a book
Do you have a book? --> Did you have a book?

I've got a book --> I had a book
I haven't got a book --> I didn't have a book
Have you got a book --> Did you have a book?

Yes, in the past we can't use GOT