You are correct....
(But you must remember that "normalizing" is a very general term which really just means "adjusting a bunch of stuff to all be at some standard level".)
In general, normalization usually is applied to audio signals such that the loudest peaks are reised to 0 dB (or some level near it).
If you look at it one way normalization is the process of very carefully eliminating unnecessary headroom.
The purpose of having headroom is as a safety margin.
The reason you leave headroom in a recording is so that, if a few peaks are a little louder than you thought they would be, your recording won't clip.
However, because the noise floor occurs at some fixed level, when you reduce the overall level to leave headroom, you reduce the S/N ratio.
(Not to mention the fact that, if you're talking about a radio station, your broadcast becomes a tiny bit less loud compared to your competitors.)
Therefore, once your content is finalized, the final step is often to raise the overall level such that the loudest peaks are "as high as they can be without clipping".
(At this point, since you know there will never be higher peaks, there is no reason to leave headroom... so it is removed in order to optimize the S/N.)
In the old days, you would carefully adjust the levels manually until the loudest peaks were just under the loudest possible level, which would be the loudest safe level you could use.
However, with an old style analog system, that actual maximum point might be somewhat vague - for example, with tape or vinyl, due to record EQ, the maximum level varies with frequency.
Therefore, you would have to run the entire file, carefully detect the highest peaks, then leave a little extra headroom to allow for any slight errors you might have made.
With a digital system, since you actually have the numerical value of every sample, there is a very well defined maximum level - "0 dB".
In most digital editors, when you select "normalize", you actually get to enter a number.
The program then scans the entire file, finds the highest peak level in it, and raises the overall level such that the peak is adjusted to become the level you selected.
(So, if you "normalize to 0 dB", the program scans the file, finds the highest peak level, then raises the level of the entire file equally such that the loudest point is at a level of 0 dB.)
However, in some cases, you might decide to normalize to a different value.
For example, some digital systems actually do have issues at exactly 0 dB, so many editors prefer to avoid actually going to 0 dB, and normalize to -2 dB or -3 dB.
The idea of normalizing can also be viewed at different levels.
For example, you could normalize the levels of all the songs on a CD such that the highest peak on
each song is at -2 dB.
Or, instead, you could normalize the level of the entire CD so that the loudest peak on the loudest song is at -2 dB.
In that case, you would say that the entire CD was normalized to -2 dB, but the individual songs were not normalized, because you prefer to preserve the level differences between them.
But, yes, saying that "you had normalized the level to 100%" is normally equivalent to saying that you "normalized to maximum level" or "normalized to 0 dB"....
I suppose someone might use the expression to mean that they had "completely" applied the process of normalizing the levels...
(As compared to "partially normalizing the levels" - which could mean "moving the levels closer to being fully normalized while still leaving some variation".)
I guess I don't understand what normalization does under the hood. I always thought 100% was raising the peaks to the edge of clipping. I assumed that was zero.