A fillet rounds an edge with a radius (R); a chamfer slices it flat at an angle, usually 45°. Both look like they're doing the same job — softening something sharp — but the reasons and manufacturing paths differ.
A fillet is comfortable to hold, keeps paint or coating from peeling at the edge (a sharp edge gets a thin, fragile coat that chips first), and in injection molding reduces stress concentration so the part doesn't crack right there — which is why almost every inside corner of a plastic part is filleted. A chamfer, by contrast, self-aligns a part into a hole during assembly, is often cheaper to machine (a simpler tool path than a fillet on a mill), and reads visually as "precision-machined" on metal parts.
In CAD, switching between a fillet and a chamfer command on the same selected edge is a routine move, and changing the value — radius, or chamfer distance and angle — parametrically updates the whole model.
When to use
Fillet edges that hands or fingers touch; chamfer edges that need to self-guide assembly or where machining cost matters.