Start with what you cook most, then work down the list. The details below are what separated these four models.
Capacity and how many people it feeds
An 8-quart basket feeds a family of four comfortably and can stretch to more for a party. Gourmia's own figure for the GAF824 is up to eight people, and the newer GAF823's 8-quart basket holds a whole chicken. Cooking stays single layer, since the included insert doesn't add a second level. If you often cook for two, a smaller basket will save counter space.
Window vs no window
A window lets you watch browning without opening the drawer, which keeps heat in. The GAF858 and GAF824 have one, with an interior light. The GAF856 and GAF838 don't. The trade-off is upkeep: window glass hazes unless you wipe it now and then.
Presets and controls
Preset counts run seven on the GAF858, eight on the newer GAF823, and 12 on the GAF824, GAF856 and GAF838. In practice, air fry, bake, roast, reheat and dehydrate do most of the work. The extra presets are shortcuts, not new abilities. What matters more is a display you can read at a glance and a preheat prompt you can trust.
Power (1700W) and temperature range
All four models sit in the 1700W class, so preheat speed and power draw are similar. Temperature is where they differ. The GAF858 runs from 90F to 450F. The GAF856 runs from 90F to 400F, and the GAF824 sits in the same 400F range. The extra 50 degrees on the GAF858 helps with searing and crisping skin.
Cleaning and dishwasher-safe parts
Every model here has a dishwasher-safe nonstick basket and crisper tray. The coating lasts longer with gentle hand-washing than with dishwasher cleaning. On the window models, wipe the glass on a schedule. The same soft-sponge habit keeps the coating intact.