Whats the difference with Carry Look Ahead Generator & Block Carry Look Ahead Generaor
They are ALMOST the same.

The difference, as you pointed out, is in fact in P* and G*, that are used to put this Block CLAG in a cascade with others. Basically, the G* out is enabled when the Carry bit result to be generated inside the circuit (in fact, you can see that P* is not added, but created removing the propagate input from the last carry generator G*).

So, instead of creating all the carry bits from the inputs, allows to be stacked and generate the Propagate (P*) and Generate (G*) for the block itself.

The advantage is a simpler logic, because to expand the 4-bit that you have you would have an explosion of signals and gates, that you pay with a (in this case) slower circuit. Note that if you pipeline it in your adder, you will have less routing and less gates, that can result in a faster circuit.