Russia OTOH did indeed use the "liberate" rhetoric wrt Ukraine, but at this point it made it clear that it intends to annex all territory that it can occupy.
It should be noted that the word "liberate" in a military context has a very long history in Russian war propaganda specifically, which is a big reason why they keep using it. It is an immediate call-out to WW2, which has a near-religious status in Russia, but even beyond that, e.g. the 1939 partition of Poland with the Nazis and annexation of West Ukraine and Belarus was also described as "liberation" then.
Now, Russia has done this already in Georgia: they consider two territories under their occupation independent states, and not part of Russia.
USA does things differently: after establishing military control, it gets local businesses bought out by US companies (investment, right?) while they are struggling, and attempts to influence political landscape.
I'd certainly choose US approach over the other, but ideally, we'd get neither.
Their troops were in fact in Iraq, Afghanistan, Syria, Serbia...
This does not excuse the atrocities and conquest as performed by Russia, while it's true USA does worry about optics much more (i.e. their presence in Serbia was a lot more toned down than in Iraq or Afghanistan, as Serbia is a European "culture" similar to the rest of Europe).
US go-to is "liberating" a territory, which is — interestingly — the same excuse Russia is using in Eastern parts of Ukraine (and which is why it's likely working with most of their own population, obviously helped with media control).