What is the best (or correct) way to wire outlets in the middle of a circuit?
1) Using the screws available in the outlet to "extend" the circuit wires to the next outlet.
2) Making a derivation from the wires to the outlet.
We also have here derivation connectors that look like those, but the take a lot of space in the recepctacle box:
The outlets we use here have this kind of connection screws
Best Answer
When wiring multiple outlets on one circuit, whether splicing or chaining is the better way depends on whether your devices are made to be chained.
If you are using North American type devices, your second illustration is the best way, even though it requires the two wire nuts (or other splice connectors) ("splice"="derivation"). It is not good to rely on the tab or other connections inside a N. A. device.
If you are using devices like the one in your fourth picture, then you do not normally use splices. For the middle outlets, you can use the two wire positions on each terminal to chain the outlets together, similar to your first picture.
I live in the U.S. but I have seen pictures of switches, outlets, and ceiling light rosettes from the U.K. and Australia that have multiple screw terminals electrically joined, and are made to be chained. Some outlets used in the U.S. look like they could be chained, but they're not really designed for it and often fail in ways that are difficult to diagnose.
Your first illustration is correct for the kind of outlet shown, which seems to be a GFCI protected outlet. These usually have two screws labeled "LINE" and two screws labeled "LOAD". These labels are not shown in the picture but I guess the top screws are the LINE and the bottom screws are the LOAD.