The only general answer to your question is "it depends" ... on many things including which manufacturer, age & control systems, engine type (2- vs. 4-stroke), etc. The engine gurus can give you chapter and verse for specific models and manufacturers.

For cars, most turbos are now designed to make them easy to live with in stop and go traffic rather than for maximum power output. Turbos designed for maximum power (such as old Porsche turbos) are relatively large and high-boost, and can have major "lag" problems on throttle opening followed by excessive power when spooled up. Hard to live with off a race track, and difficult to handle on the track, because of the non-linear throttle response. Modern gas engine turbos in normal vehicles are relatively small and don't produce very much boost - but can produce with very low (just off-idle, even) gas flow so they work right away. Another consideration on-road, of course, is emission control - the old Porsche method was extremely dirty especially at full throttle (lots of fuel) and low engine speed (little air), while modern systems have to be much better controlled.

Come to think of it, some locomotives have the Porsche issue, too: "honorary steam locomotive" Alcos?

Remember the purpose of supercharging (of which turbo is a variant): pump air into the engine, rather than just relying on the vacuum normally produced by it. More air = more fuel can be burnt = more power. That's true for practically all 4-stroke engines, but some 2-strokes produce relatively little vacuum or have port systems that need pressure; they have a supercharger of some kind just to run.

Again, the gurus will have specifics and examples.