As you can see, the components are the same, but the battery is now placed inversed. Since there are DC-blockers at the input and outputs, this doesnt matter for the normal functioning.
Remember that in small signal analysis all the indempendent voltage sources are shorted. It only rests the model for the transistors but if you take a look at the next image, they actually have the same behavior (only the conventions are changed). So, as you can see, both circuits have the same model.
As it says, the small signal model is a... model. Models serve to solve problems that usually cannot or are too difficult to be solved by simple mathematics, however they work for certain conditions. For the small signal model, the condition is that all the signals involved be small (hence the name os the model) in such a way that the transistor does not go out of the operation point.
So the only diference between these circuits happens when you try to amplify something that saturates the output, and thats why we have lab classes with this subject.
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