Amber has a distinctive golden or coppery quality that light brown generally doesn't reach — a clarity and vividness that reads almost as if the iris were lit from within. Light brown reads as a more conventional warm brown: the same broad family, but without the saturation that makes amber noticeable enough to be commented on.
There's no fixed threshold for how golden a brown iris has to be before it's called amber rather than light brown — this is a genuinely subjective call that varies by source.
Warm lighting or white balance can make light brown eyes photograph as amber, and cooler light can make amber eyes look more like ordinary light brown.
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.