Equivalent noise simply represents a noise source (current, voltage, or resistor) at the input, output, or any other terminal of a noiseless circuit, which replaces the existing (real) noise at the respective otherwise open terminal of the real circuit.
Hence the equivalent input noise is identical (or equivalent) to the input noise of the open input circuit (meaning: no other noise sources present than that/those from the circuit itself); accordingly the same is valid for the open (no load) output, or any other open terminal of the circuit.