Re: LC oscilator type
I think both are Colpitts oscillator. One major difference is in how transistor is biased. One is fixed biased and other one is biased with voltage divider and an emitter resistor for stability over temerature. I think second figure is more standard. In that figure inductor is connected across the nonconnected ends of capacitor C1 and C2. But can see that in first figure it is same in ac analysis. In ac analysis, DC power supply will be shorted in sense. I think capacitor C3 is used to isolate the DC conditions in base of the transistor from the feedback network.