Login?

I may be making life more difficult for myself just by thinking but I am confused as to whether or not this can even be done?

I would like a login specifically for my site, not necessarily for WP but purely for my site. So that when a user comes to my site they arfe able to register, and routinely login – by doing so I would also be able to manage the Users and where they can access the site.

Is there a plugin or a way that this can be done?

I realise I may be being a n00b but cant find the right words to search on Google as I am not sure that this even exists.

Kind regards