1: There are two types of Pentium 4's: with and without hyperthreading. A hyperthreaded Pentium 4 can operate on two threads at the same time.
2: Dual-cores are CPU's with two physical CPU cores.
3: There are significant differences between the Pentium4 and Core2 architecture, so that even at the same speed, the core2 will always be faster. [EG: A Core2 Solo at 2.5Ghz will be faster then a non-hyperthreaded Pentium4 at 2.5Ghz, as the Core2 does more work over the same time span].
4: Core2 chips tend to draw less power and emit less heat then the Pentium 4 architecture.