Wind chill is how cold the air feels once wind is accounted for, and heat index is how hot it feels once humidity is - both use the official NWS and NOAA formulas. The thermometer alone misses this - wind steals heat from your skin in winter, humidity blocks sweat from evaporating in summer. Both use the official US National Weather Service formulas, not an approximation.
Wind chill only applies at or below 50°F with wind above 3mph - the National Weather Service defines it specifically for that range, since wind doesn't meaningfully change how warm air feels the same way. Heat index is really only meaningful once the combined effect crosses about 80°F - below that, humidity barely changes how the temperature feels. Outside either range, this shows the plain temperature instead of forcing a number that wouldn't mean anything.
Both formulas come directly from the US National Weather Service and NOAA - the same equations used in official forecasts and heat/cold weather warnings, not a simplified approximation built for this tool specifically: NWS Wind Chill → · NWS Heat Index →
The heat index category boundaries used here - Danger starting at 103°F, Extreme Danger at 125°F - are NWS's own precise operational thresholds. You'll sometimes see rounder figures like 105°F and 130°F elsewhere; those are a popularized simplification, not a different standard.
Wind chill is how cold the air feels on exposed skin once wind is taken into account, because moving air strips away the thin layer of warmth around the body. It is calculated from air temperature and wind speed using the official NWS formula.
The heat index is how hot the air feels once humidity is taken into account, because humid air slows the evaporation of sweat. It uses the NOAA formula and is only valid above about 27°C.