It can freeze faster-- the Mpemba effect it's called. It doesn't always happen.
http://physicsworld.com/cws/article/print/24493
Some things contribute. For example, evaporation means there is less to freeze. So when it gets to zero, there is still alot of energy to go to freeze it, so the one with less could freeze faster. I don't think this one is the exclusive, main, answer based on some websites that claim experimentation suggests something else is doing it too--it happens with closed containers I believe I read). I haven't tested this yet. (working on it)
Gas loss may also affect it (when you heat the water, there's less dissolved gas).
Also if you use hotter water, the tray cups hold less mass of hot water cause hot water takes up more space, has less density.
Other than gas loss, it probably has to do with convection currents, or insulation difference.
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EDIT: Some people say that it is because of the freezer sensing the heat, making it turn on, making the temperature colder. OF course this could contribute if you're testing them separately.
I plan to use outside next winter to eliminate that. Or in the freezer I assume I can put them in at the same time and that would work?