A homographic solution is one in which the configuration of all the masses is preserved for all time. One example of this are the relative equilibrium solutions. Each mass rotates at a fixed distance from the center of mass at constant angular velocity. For the 3BP these are the colinear solutions found by Euler and the equilateral triangle configurations found by Lagrange. A homothetic solution is one in which the scale size changes while retaining the configuration and no rotation is permitted. An example of this would be a total symmetric collapse: start 3 equal masses from rest at the vertices of an equilateral triangle and they will retain the configuration as they collapse to the origin. Both of these solution types are examples of central configurations. Saari talks about these things extensively in his book: "Collisions, Rings, and other Newtonian N-Body Problems"