What's the difference between a slicker brush, an undercoat rake, and a deshedder?

Across the reviewers we read, a slicker brush (fine bent wires) lifts loose hair and light tangles from the topcoat, an undercoat rake pulls dead undercoat from thick double coats, and a deshedder uses a fine-toothed blade edge to grab shedding hair near the skin. Many owners end up owning more than one because each addresses a different stage of shedding or matting.