What is better an Intel Pentium III or an Intel Celeron?

Celeron doesn't refer to any particular processor series. Celerons were cost-reduced versions of their Pentium equivalents. The Celeron in question could be based on a Pentium 2, Pentium 3, Pentium 4, Pentium D, or Core 2 Duo. In which case the answers would be "Pentium 3, Usually Pentium 3, Celeron, Celeron, and Celeron", respectively.