Both of these are mentioned in the Austrian economics literature but they are quite different. Conceptually they are both models in the sense that they are attempts to picture certain conditions for the purpose of gaining insight into how the economy works.
Evenly Rotating Economy
"The evenly rotating economy is a fictitious system in which the market prices of all goods and services coincide with the final prices. . . In reality there is never such a thing as an evenly rotating economic system. However, in order to analyze the problems of change in the data and of unevenly and irregularly varying movement, we must confront them with a fictitious state in which both are hypothetically eliminated. "
"The only method of dealing with the problem of action is to conceive that action ultimately aims at bringing about a state of affairs in which there is no longer any action, whether because all uneasiness has been removed or because any further removal of felt uneasiness is out of the question. Action thus tends toward a state of rest, absence of action."
"The essence of this imaginary construction is the elimination of the lapse of time and of the perpetual change in the market phenomena."
For all intents and purposes the use of the words 'imaginary construction' is conceptually just another way of saying the word 'model.' The chief characteristics of the model of the evenly rotating economy are given above.
In contrast, the concept of the unhampered market as an imaginary construct (model) has as its chief characteristic only the elimination of economic interventionism. All of the natural processes and the natural laws and economic laws that pertain to human actions are permitted full expression in this model.
The essential difference between these two conceptual models is that the evenly rotating economy is one that is in the state of equilibrium whereas the unhampered market is in the state of disequilibrium. Since the economy is always in the state of disequilibrium the unhampered economy conceptual model is significantly more powerful.
Those familiar with the literature of Austrian economics may then wonder whether this powerful model of the unhampered economy has ever been further advanced. The answer is yes. It has been explored and explained further using deductive reasoning and logic by many of the great Austrian economists. I am aware of no more penetrating and complete exposition of the unhampered market model than the divine economy model and the divine economy theory.