Why does comparing strings using either '==' or 'is' sometimes produce a different result?

Two string variables are set to the same value. s1 == s2 always returns True, but s1 is s2 sometimes returns False.

If I open my Python interpreter and do the same is comparison, it succeeds:

>>> s1 = 'text'
>>> s2 = 'text'
>>> s1 is s2
True

Why is this?