so to me, its quite obvious that the right is a Common emitter with Re..

However on the left diagram, I'm really not sure if its Common emitter with Re.. I know for a fact its a common emitter, but my teacher told me since we only care about the AC model, the emitter path would just take the path of the capacitor (which is short circuited therefore there would be no emitter resistance)

If that is correct, (that the left diagram is just a CE without Re), then how would the DC bias model be treated? I included an Re in the dc bias model but as far as the equations given to us (as far as Av and Rin, Rout , etc.) I treated the actual circuit like a regular CE. Can someone please clarify this for me? I would really appreciate it. Thank you!

 

Basically, for AC analysis, anything in parallel with the capacitor can be ignored. For DC, ignore the capacitor.