Richard Fry wrote:
"It doesn`t matter whether we state the result of measurement in units
of SWR, return loss, or as a reflection coefficient -- they all give the
same information -- ."

Correct. The units above are fungible. All are an expression of the
mismatch of a load to the Zo of the transmission line.

With a Bird wattmeter, the reflection coefficient (rho) is the sq. rt.
of the reflected power divided by the forward power.

SWR = 1+rho / 1-rho

Return loss in dB = 20 log (rho)

Return loss in dB = 10 log (Ref.Pwr./Fwd.Pwr.)

Rho = (ZL/Zo)-1 / (ZL/Zo)+1

None of the expressions above include the source Z, therefore it does
not apply.

Best regards, Richard Harrison, KB5WZI