Can you log in with a google account in iphone?

So you know how in androids if you download an app and it might say "log in with google account" or "sign up with google account" e.g. Pinterest. But how does that work in a iOS? Do apps downloaded from the apple store in iOS devices have that "log in with google" option? If not then is there an alternative for logging in with a google account? I usually sign up in apps (often games) with my google account but if that doesn't work on iOS devices does that mean I have to start over and make a new account that is compatible with iOS?

Yes. No problem.

It is entirely up to the app to decide how they let you log in.
with Androids, most of their built-in apps are owned by Google, since Google made the Android OS. So if you are using a Google app on your Apple device, you sign in with Google.
otherwise it is up to the app maker.