Normalization means adjusting the waveform’s amplitude to some level. That’s a precisely defined operation, an objective measure. But “loudness” is a different and perceptual thing. It’s a measure of “how loud” something feels to us, and I understand it depends on the overall dynamics and frequencies, and you can attempt to measure it through different algorithms / heuristics.

The loudness war wasn’t about normalizing to 0db vs -3db, but rather about dynamic compression which is a process that raises the volume of softer sounds without affecting the loudest ones as much (or at all). It’s what you use to make the breathiness of a singer’s voice, or a drum kit’s hi hat, more present in a recording.