I think they're both correct. This is way more in-depth than is necessary for the DAT but basically the sodium channels have 2 gates.
Na+ gate #1 opens and Na+ ions rush in --> K+ channels open and K+ rushes out --> Na+ gate #2 closes, preventing Na+ from rushing in --> K+ keeps rushing in, leading to hyper-polarization --> Sodium-potassium pump restores concentrations and resting potential across membrane
One of the gates is called "activation gate" while the other is called "inactivation gate" (this is the one that closes after the first one).