Doc
Well, from my (rather quick and brief) web search, it looks like while Japanese people might move around more, you still were correct when you wrote
Doc they would do the job their father/mother did. This led to families running the only business of a particular skill for generations.
I'll just copy-paste what I have:
In medieval Japan, social mobility was much more rigid than in Europe. For example, while samurai were some of the most revered members of Japanese society, they did not own land. On the contrary, in Europe, knights were also highly respected, but they were often paid in lands for their services to the Crown, which produced a completely different power dynamic.
In turn, this means that Japanese samurai were much less socially powerful than knights, and because most people in medieval Europe, through fortune and lots of luck, could work their way up the social hierarchy to become a knight, this gave medieval Europe the edge in terms of social mobility over medieval Japan.
However, it was not just military social mobility that was possible in medieval Europe. Social mobility was possible through trades. In medieval Japan, peasants gave birth to the next generation of peasants, while lords and ladies gave birth to the next generation of lords and ladies, and so on.
In medieval Europe, while this was the case most of the time, there was a much higher chance of climbing the social ladder. A peasant could give birth to a peasant child, but if that child showed certain military prowess, or was a skilled blacksmith, or even traded well at local markets, they could carve out a career for themselves in one of these industries. Merchants who ran mini-trading empires in medieval Europe, such as those operating from port cities like Genoa, often came from very poor backgrounds themselves, but worked their way up the social ladder.
So while japanese might have had more chances at changing places, europeans indeed seem to have had... had have... more chances at changing trades.