You're getting a little confused.

Un-boosted ISO

Or what you're calling "native range." There's a native ISO setting, which is what the sensor uses without any amplification, and you can consider this the "base" ISO setting of the camera. All of the unboosted other ISO settings are achieved by amplifying the gain on this native signal.

Boosted ISO

Boosted ISO settings, otoh, aren't done with signal amplification. They are achieved by in-camera digital processing of the data after the image is taken. If the boost is in the higher-ISO direction, the unboosted setting used is the highest one available (e.g., if you have 'native range' from 200-6400, and 12800 and 25600 are your boosted levels, then you're really using 6400 amplification on the sensor), and the image is underexposed by the additional stop(s) for the boosted level. Then the image's exposure is adjusted 1 or 2 stops brighter in the in-camera processing. But the cost is that you will have increased noise--more so than with only amplification.

If the boost is at the lower levels (e.g., iso 100 or iso 50), then the signal used is the native/base ISO, the image is overexposed by the stop(s) needed, and the exposure is adjusted darker in post. But the cost here is decreased dynamic range.

This distinction is why they are careful to label the digitally boosted settings as such--unlike the amplified signals, you have additional tradeoffs to consider before using them (like digital zoom).

Canon vs. Nikon

The other thing to keep in mind is that Nikon uses amplification for the entire unboosted range, but Canon doesn't. Canon also uses the digital push/pull processing for their 1/3-stop settings--that means you're losing dynamic range on the -1/3EV settings, and gaining noise on the +1/3EV settings. This is why you'll sometimes run across the advice for Canon shooters to keep your iso on the full stop settings or use the -1/3EV settings.