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I read that for a given N-port network there are two different conventions about defining the incident and reflected waves.

This is the first convention:

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This is the second convention (we see that there is a normalization with respect to the characteristic impedance of each line connected to each port; in general we assume that these lines do not have the same characteristic impedance):

enter image description here

In both cases Scattering parameters are defined in this way:

enter image description here

My question is this: is the Scattering Matrix the same for both conventions, or should we find it in both cases? If it is different, when we see S parameters in devices datasheets, which is the convention used?

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The numbers in the matrix will be different. If you find the matrix with a particular normalization, you can compute it with a different normalization by multiplying.

There are three normalizations commonly used. In books on circuit theory the matrix is often normalized to one ohm.

For RF work with real devices, most scattering matrices are referred to 50 ohms.

If you are working with cable tv or something, the normalization will be to 75 ohms, as the cables used with these devices have that characteristic impedance.

The theorems involving the s matrix (for example, unitary=loosless) will be true no matter what the normalization used.

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