What is the difference between hypertrophic scarring and a keloid?

The area affected. Hypertrophic scars are raised scars that do not spread beyond the boundry of the original scar. A keloid is a scar that continues to grow, extending well outside the boundary of the original scar site. That is, it spreads into areas of previously normal non-scarred skin.
Local spread. The definition of a keloid is overgrowth of the scar tissue into the surrounding tissue over the boundaries of the scar. Different from a hypertrophic scar which is simply a thickened scar, remaining within the boundaries of the original scar. It can continue to grow, see my answers in how to treat safely and without stimulating further growth. Mostly do not allow anyone to cut it, without a plan.
Scar types. Many people confuse keloids with hypertrophic scars. The latter are more common. By definition, a keloid scar will grow past the border of the scar, so if it looks like a cauliflower (top bigger than base), it's a keloid. A hypertrophic scar is simply one that is thick. It can be really thick but if the base isn't smaller, it's hypertrophic. Keloids are way harder to treat than hypertrophics.