What are the differences between a set of Pocketwizards and a set with a wireless transmitter and receiver. Don't they do the same thing?
Radio flash triggers are a type of device. PocketWizard is a specific brand of radio flash trigger. So, yes, they do the same thing. But while all PocketWizards are radio flash triggers, not all radio flash triggers are Pocketwizards.
In addition, PocketWizard has the highest reputation for reliability, and are the oldest radio trigger brand that's still on the market. Their triggers are built in to some Sekonic flash meters. And they have the best backwards compatibility with older units, but in order to retain this compatibility, they're using the same radio frequencies they always have. From the PocketWizards website:
In North and South America (and some parts of Asia) we use the 340 – 354 MHz range because it is the least crowded frequency range for our class of wireless triggering devices. Other choices like 433 MHz, 900 – 930 MHz ISM band, or the 2.4 GHz band have many more interfering devices on them.
Most of the newer, less expensive triggers that you see operating on 2.4 GHz, because it doesn't require licensing. But it's also where Wi-Fi and Bluetooth operate.