The Hanukkah menorah or Hanukkiyah was inspired and influenced by the lamp known to the Jews as ner tamid, (A Ner Tamid is an eternal lamp. Ner is a light, and Tamid is eternal that hangs above the ark in every synagogue) which came with the famous story of the rededication of the Temple after the successful Jewish revolt against the Seleucid monarchy and the miraculous jar of oil that burned for eight days, which should have only lasted for day.
Hanukkiyah is a candelabrum, but is different from a menorah. Although menorah is also a candelabrum, the difference is, menorah, has only seven branches, while a hanukkiyah has eight branches in a row with an extra holder most of the time placed in the center, placed a little higher than the others with four of the other candles on each side. Though no matter how you look at it, hanukkiyah is the same as a menorah.
On the first night one candle is placed in the holder on the far right, and is usually lit using the Shamash. (Lead candle) One light is kindled, and on every successive night an additional light is added so that on the eighth night, eight lights are lit. The candles are placed in the Hanukkah menorah from right to left and lit from left to right.