Identifying bjt amplifier circuits configurations
Both methods that you described are useful for identifying the single transistor amplifier configuration.
In the first approach, you can identify the amplifier configuration by one transistor terminal being connected to small signal ground. So this could be the actual GND symbol or a constant potential like VCC in this example.
Your second approach tries to identify the signal input and output terminal of the transistor. Once those terminals are identified, the remaining terminal is the common terminal. In this case, the input signal is applied to the base and the output terminal is connected to the emitter. Forget about the reference point when using this approach. In the end, input and output signal can be referenced to the common terminal anyway.
Both approaches lead to the same result.