You say Coliseum, I say Collosseum

I know that the name Collosseum, in Rome, originated as a nickname for the Flavian Amphitheatre, because of a Collossal statue that stood nearby. But in L.A.
we have the Coliseum. Why the different spellings, and do they have different etymologies?

The OED says that they are variant spellings of the same word. Both have been used in the past to refer to the arena built in the time of Vespasian.