Are you just wikipedia-ing stuff and trying to sling it together now?

If I say that it changes saturation, I literally mean that the saturation of the pixels has changed.

Then

In this case, I'd take away from the yellow tint, which does affect the individual pixels' saturation values as it wouldn't really be white balancing without that, and it could be used as part of fixing the portrait.

I feel like you're redefining stuff to make it fit your narrative at this point.

It can achieve an effect not unlike a color balance adjustment

De-saturating a color channel is not color correction. Maybe this is where you are having a disconnect in white balance and saturation.

You can falsely color balance a photo by de-saturating a channel. It is a trick editors use all the time when you have multiple color light sources and shifting the color wont really fix the problem. The issue is that it can easily become washed out.

For interior photography it's fine, because people are used to interior photos looking really minimal with color.

http://static1.squarespace.com/static/55e108c6e4b0c45c79d4c221/56f166c327d4bd21a4ac6153/56f987c3f699bbe615972840/1459193935188/homepageextras-3.jpg?format=1500w

This photo for example, had yellow light, blue outside light from a cool winter morning, orange lights off in the left kitchen, and to balance it out, the best way to correct it without a lot of select area editing, you balance for the yellow light, and de-saturate the blue.

It's still not color balancing though.

http://static1.squarespace.com/static/55e108c6e4b0c45c79d4c221/56f166b98a65e24b7289e925/56f986c817110754558296e7/1459193694945/homepageextras-48.jpg?format=1500w

Here is an example where it looks a little flat. Because there was orange light, mixing with blue overcast light from outside, a little bit of green coming in from the back window of the kitchen, and yellow lights above the counters in the kitchen.

The client was happy with the work, because it looks like interior photography, but it wouldn't work as well with something like a person.

Again, color balancing is about shifting colors. Most commonly in photo is shifting from blue to yellow or green to magenta. If you simple de-saturate a channel, that is not color balancing at all.

It's frustrating that you nitpick what I say but then use expressions like "overall saturation" without explaining what you mean by them.