Cessna models 172R vs 172S

The flight school that I am about to start taking flight lessons has a Cessna 172S; when I go into their website and check out the Cessna 172s POH, I see that that the POH has a different model (Cessna 172 -R). 

This is a bit confusing for me because shouldn't they be using a Cessna 172 S-POH and not a 172 R POH. 

So, I begin investigating a Cessna 172S POH and found they are similar (unless im looking at an old expired revision POH)

Although, both POHs might look a bit similar, there is a difference for example, in the Horse Power Rating and Engine Speed. 160 HP vs 180HP

My question to this is the following:

Why would they post a POH's different model? Could this just be a mistake from their side? Or if they posted that POH  just as a reference to study, - is that even something smart to do?  (to me just does not sound right)  

I am aware that the FARs required for the POH to be on board any time. - But still why would they put that POH that is different from the currently model they are flying. 

Before, I give them a call in regards to this, i wanted to see if anyone had further input. 

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