Most transponders in competitive sports, and certainly most pro cycling events, will be an active type, i.e. they include their own power source. The timing mats are relatively simple EM trigger loops that induce the transponder to wake up, yelp its identity (typically on UHF frequencies) to the trackside receivers that will actually record the passing time, then go back to sleep. Such systems generally remain reliable even in large passing groups. Commercial prices vary, but the trackside equipment (mat, decoder, laptop, software) typically costs a few thousand dollars, and the transponders ~$100 each with a lifespan of 5 years.
Some manufacturers claim millisecond accuracy, which is plenty for (say) counting laps in cyclo-cross, or for timing many BMX events; but they're not enough to distinguish the places in a >70km/h field sprint for the finish line.
Some mass participation events like public marathons may use low-cost/disposable passive transponders e.g. ones embedded in the bib number; these are more like a typical RFID chip, having a longer (and rather jittery) wake-up time, in part because they draw power from the mat itself, and a much lower transmission energy. They're more easily disrupted by environmental conditions, or when passing in large groups, or even by sweat & skin contact.
Telemetry from onboard bike computers and sensors is indeed a completely separate stack, and can be anything from a bluetooth relay by phone app over cellular, to a dedicated vendor-specific box with its own SIM card and a short-range radio to signal the team car. The onboard sensors are generally using ANT or BTLE to talk to the head unit aka "bike computer" that aggregates, records, displays, and relays the data. Speed may be calculated by GPS/GLONASS/etc, or sensed by wheel rotations e.g. using a spoke magnet or even hub-based rate ticker, in which case the necessary measure of precise wheel diameter may still be calibrated by the head unit using GPS. Power is not measured directly but inferred e.g. by integrating a dynamometer within the crankarm to compute power from strain & cadence. Some units also capture barometric pressure to estimate altitude, and this may be considered more accurate than GPS right up until you ride through a pressure front and it goes bananas. Some bicycles e.g. those with electronic/wireless shifting may also report their current chainring & sprocket selection, and finally you can overlay all this excruciating near-real-time detail onto the Gopro video feed from your handlebars/seatpost cameras and livestream it over cellular networks and thence to the world-wide peanut gallery.
To sum up, there's an awful lot of 2.4GHz activity going on in the pro peloton, and I hereby deny ever having paired a second bike computer with the HR strap and power meter of my nemesis in order to know when the bastard was too tired to follow my attack, no sir
