is a theatre. The seating forms a semi-circle, or slightly more, around the performance area.
This
is an amphitheatre. The seating forms an oval around the performance area.
The terms 'amphitheatre' and 'theatre' apply to two distinct types of building, and are not interchangeable, even if gladiatorial games were held in both.
And while we're at it, this
is not a 'colosseum' (or 'coliseum').
This
is the Colosseum. There is only one.
(This inspired by my recent trip to Turkey, where I found theatres at Side, Aspendos and Fethiye all labelled as 'amphitheatres', even in respectable volumes like the Dorling-Kindersley Turkey guide. They're not. There was even a little open air theatre in the hotel we were staying in, and that too was labelled as 'amphitheater'. Yet curiously, I saw no fights or wild beast hunts all week.)
