You may cast spells from your hand without paying their mana costs.
There are obvious differences in what cards are free, like the aforementioned Aluren that only allows creatures of converted mana cost 3 or less, but the cards all contain some form of the phrase "without paying their mana costs".
Contrast this with Rooftop Storm, which reads
You may pay 0 rather than pay the mana cost for Zombie creature spells you cast.
Now obviously, if you ignore the restrictions on the three cards I've mentioned, they all allow you to cast certain cards for free. But why does Rooftop Storm phrase its ability in this way? Are they functionally different in certain situations?