What is the main difference between a dual-core 2.4GHz and a Quad Core 2.4GHz processor?

[Matt]

Yes...and no...
Both the dual core and quad core will run at the same speed, if they are a 2.4 GHz processor.
A dual processor has two cores, while a quad has four cores.
A quad core is far more efficient and stable, however, than a dual core processor. Most applications require only one core to run, but in terms of professional software and games, they may require more than one core.
This is why quad core is better; a game or professional app will have extra cores to run perfectly, rather than a dual core processor, which would cause instability and lag.
In terms of opening up an application like Internet Explorer, they would open at the same speed.