What if I switch the place of the load in a common emitter NPN transistor circuit?
Then, in the second configuration, I moved and put the load between the emitter pin and GND. I have never seen this configuration where the load is at the emitter pin,


You've created what's called the common collector configuration. It's also called an emitter follower. It's very common and well-known.


  Is there any advantages or disadvantages between the two configurations? In my opinion, it seems to work just the same way,


They really aren't the same at all. Where the common emitter has (potentially) voltage gain and high output impedance, the common collector has voltage gain very near 1, and low output impedance.

The common collector circuit is typically used as a unity gain buffer (no voltage gain by can produce more power output than is input). The common emitter is typically used as a voltage gain stage.