First, that map is a forecast, showing where conditions are favorable for turbulence developing. It doesn't mean it *will* exist. Although I see forecasts in the US for moderate turbulence all the time, it's quite rare that I actually experience it.

Second, the second map you posted is for a huge altitude range - FL200 up to FL450. Within that range, there are likely to be altitudes that are smooth. Most pilots will try to find those. Bouncing around is uncomfortable for them too - makes it difficult to tune radios, write, read, drink coffee, etc. So they will usually do what they can to search for smooth air.

Ultimately, you never really know what you're going to get. Those maps can help, but they are never a guarantee.