Using Django User Model

I've seen people using the default django user model as a foreign key in two ways:

1)

from django.contrib.auth.models import User
user = models.ForeignKey(User)

2)

user = models.ForeignKey('auth.User')

but when implementing one-to-one relation I've only seen:

from django.contrib.auth.models import User
user = models.ForeignKey(User)

I have two questions regarding this:

1) Are the two ways to define Foreign Keys practically the same?

2) Can you use user = models.OneToOneField('auth.user')?

Thanks in Advance!