The Aztecs came from Aztlan the place of their origin. Aztec in Nahuatl means the people who came from Aztlan.
The Aztecs who left Aztlan had wandered for many years and finally settled in Coatepec (Snake Hill in Nahuatl) near Tula. There the Aztecs built a city and lived for many years. When the Aztecs were in Coatepec, a dispute arose. Some of the Aztecs who followed Huitzilopochtli wanted to leave and some of the Aztecs who followed Coyolxauhqui (Huitzilopochtli's Sister) wanted to stay in Coatepec. In the battle that ensued the followers of Huitzilopochtli won and they changed their name to Mexicas.
The Sculpture of Coyolxauhqui's dismembered body lies today at the foot of the Templo Mayor the religious center of the Mexica people.
Mexicas, therefore, are the Aztecs that split from the other Aztecs in Coatepec. The Mexicas were led by Huitzilopochtli. They continued south and founded the city of Tenochtitlan or Mexico (what is now Mexico City) in Anahuac. Tenochtitlan in Nahuatl means the place of prickly pear cactus. Tenochtitlan was also refered to as Mexico. The Empire of the Mexicas was also called Mexico. Mexicas means people from Mexico. Hence, Mexicano or Mexican means the same as Mexica, people from Mexico
The City of Tenochtitlan was built in the middle of Lake Texcoco. Anahuac or the Valley of Mexico was full of lakes at the time the first Europeans came to Mexico. Anahuac in Nahuatl means "Near the water or sea."
Tenochtitlan, like Venice in Italy, was a city built on water with many canals. Canals and canoes were an important method of transportation for the Mexicas.
In summary, the Aztecs were from Aztlan. Aztecs means people from Aztlan. Mexica means people from Mexico. Aztecs wandered until they found their new homeland, Mexico. When the found it, they changed their name to Mexica, people from Mexico. According to Dr. Alejandro Villalobos a learned expert from Mexico City, the Aztecs turned into Mexica once Huitzilopochtli appeared in a dream to four priests (Teomama) when our people settled at Chapultepec. Dr. Villalobos says the Huitzilopochtli gave his name to the Aztecs since his was also known as Mexi. So Mexica also means sons of Mexi or Huitzilopochtli. Apparently in the Mexicayotl Chronicle, Mexi is one of the names given to Huitzilopochtli.