How to implement own account system and optional google sign-in?

I have my site and I am currently in the process of rewriting the login system.

I would like users to be able to choose whether they sign in using my account system or they can use the google sign in system.

I will be storing data alongside my accounts, so I will need to store both google accounts and my own accounts inside a database.

Would the different account types need to be in a different database? Because I will store the google account "ID" , which I will not have for my own accounts.

Does anyone know a good way to do this?

Thanks!