Original: The Poincaré disc model, also known as the conformal disc model, also employs the interior of a circle, but lines are represented by arcs of circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.
Simplified: The Klein model, also known as the projective disc model and Beltrami-Klein model, uses the interior of a circle for the hyperbolic plane, and chords of the circle as lines.