Normalizing is two operations that people usually run separately: read what the file measures, then move it. The reading is an integrated loudness in LUFS or a true peak in dBTP over the whole file, and the move is a single gain applied to every sample.
Loudness or peak
Loudness mode targets the integrated LUFS reading. The signal is K-weighted, measured in 400 ms blocks, and gated so silence between phrases does not drag the number down. This is the mode that makes a set of podcast episodes or interview clips sit at the same perceived level.
Peak mode targets the highest true peak instead. It scales the file so the loudest moment lands exactly where you asked, which is what you want before handing a stem to someone else, and what you do not want when the job is matching perceived volume.
A quiet, sparse recording normalized to -1 dBTP can still sound far quieter than a dense one at the same peak. Nothing is wrong with the measurement; peak and loudness are different quantities.
The gain, then the ceiling
The gain is worked out once from the measurement and applied flat. Nothing is compressed, and the balance between loud and quiet passages is untouched.
Raising level moves the peaks with it. A file at -20 LUFS peaking at -3 dBTP needs 6 dB to reach -14 LUFS, and those peaks then land at +3 dBTP, which clips. The limiter catches exactly that case: it holds anything crossing the ceiling with 5 ms of lookahead, so the peak stops at the ceiling instead of at full scale.
Keeping the ceiling at -1 dBTP is the usual delivery rule. The headroom covers the sample values a lossy encoder shifts when it decodes, which is how a file that measured 0.0 dBTP before encoding ends up clipping on playback afterwards.
When the target is out of reach
The gain stage covers 24 dB either way. A recording that needs more than that is turned by the full 24 dB and lands short, and the rail says so rather than reporting a target it did not hit.
Loudness range is worth reading before deciding the target is the problem. A file with 15 LU of range will fight a loud target: the limiter has to work through every peak to get there, and what comes out is flatter than what went in. Lower the target instead.
Reading the projection
Both projected numbers update as the target moves, before anything renders. The loudness figure is the measured integrated value plus the gain. The true peak figure is the measured peak plus the same gain, which is what tells you whether the limiter is about to do real work or sit idle.
If the projected peak sits well under the ceiling, the limiter changes nothing and can stay off. The export is then a pure gain change and the output measures exactly on target.