Assimilation is the process of taking in new information and fitting it into a preconceived notion about objects or the world.

Accomodation means adjusting to new experience or objects by revising the old plan to fit the new information.

 

"Adaptation is a process of seeking an equilibrium between the self and the environment. This equilibrium, or equilibriation as Piaget refers to it, is a balance between the process of assimilation and accomodation." (The Piaget Primer, p.18)

"Over time, as these processes of assimilation and accommodation repeat and compound, they lead to major shifts in understanding—ushering children into a new developmental stage." (GPT4)

"Schema (pl. schemata) is a simple mental image or pattern of action, a form of organizing information that a person uses to interpret the things she sees, hears, smells and touches." (The Piaget Primer, p. 17)

In modern cognitive sciences, we more often use the term mental|cognitive|internal "representations" (C-representations = comprehension|understanding representations; P-representations = production|action representations)