That's because the calendar had two systems. It had the sacred Tonalpohualli, which was based on the 260-day cycle and the Iuhpohualli, which was a 365-day cycle (Palfrey). The Aztecs also kept the two different aspects of time, the Tonalpohualli, which was counting the days and the Xiuhpohualli (Iuhpohualli) which was counting the years (World Mysteries).  

No, they didn't use the calendar the same way we use ours. They used theirs to figure out the best times to plant crops and hunt for the best meats. They also used is as a divinatory tool. To predict the comings of their world and the end of their world.