The term overlay is extensively used in learner modeling research, especially for tutoring systems where Wenger acknowledges it as a "standard paradigm" (p.137). It has been coined by Carr and Goldstein in 1977 and defined in the following way:

"The kernel idea is to design a modular Expert program for the task, and to explain differences between the behavior of the Expert and the subject in terms of the lack, on the player's part, of some of the Expert skills. Thus, a model of the player is a set of hypotheses, each of which records the system's confidence that the player possesses a given skill. Such models are called overlays to reflect the fact that the model of the individual is basically a perturbation on the Expert's structure." (p.4)

While "overlay" would mean that one model is in some way covering the other, the definition from Carr and Goldstein restrict this relation in a way which suggested critics of this choice of term:

"An "overlay model" (Carr and Goldstein, 1977) is one in which the only possible diagnosed discrepancies are missing pieces of knowledge: RS*k ⊃ RSRL*k. The use of the term "overlay" is not ideal because of its ambiguity: "partial model" would definitely be better, but "overlay" has already a long history in ITS." (Dillenbourg and Self 1992)