Hi @remi.kalbe,
Have you taken a look at this doc:
It describes the universal login page and how it can be customized. It also describes the lock widget, which can also have some customization.
This topic addresses the options based on which platform you are building for:
Embedded login is when the login page is embedded directly in your app (this can use the lock widget or a custom UI). If you are trying to avoid a redirect or popup then you will likely need to use embedded login, this comes with some warnings because of the risks associated with cross origin authentication. It is certainly an option, but will typically take more diligence/time on your part.
Hopefully this helps clarify things, if you have more questions please let us know.
Thanks,
Dan