Amber reads as a fairly solid, uniform gold-to-copper tone with no real green component; hazel is multi-tonal, typically including some green or grey alongside brown/gold.
Because amber and light brown/hazel sit close together on a continuum, where exactly 'amber' starts is a judgement call that different sources make differently.
Warm white balance can make ordinary light brown or hazel eyes look more amber than they do in person, and vice versa in cool light.
No photograph or online colour-picker tool can definitively classify which of these categories a specific pair of eyes belongs to — classification is inherently somewhat subjective, and lighting/camera effects change the apparent result.