In some cases, these distortions are accidental (no one really wants capital investment reduced, which is the effect of even a 0.1% capital gains tax; they just consider the revenue raised to be more important than the distortion).
In some cases, the distortions are themselves the goal. Cigarette taxes are a great example -- I think the economy overall would be better off if there were 0% revenue on a $50/pack cigarette tax, as it would save health care and other costs far higher than the revenue on a $0.50/pack cigarette tax. Or, a local tax per-bag of trash produced, in excess of direct disposal taxes, in an attempt to capture the external costs of waste. (in Zurich, I think the bags are something like $5 each)
Carbon taxes could be either, but a steadily increasing carbon tax is much more like a cigarette tax than a capital gains tax.