Kunilou has it pretty close.
Traditionally, the American carmakers’ approach to quality was that as long as a part was within tolerance, it was good and could be used. The Japanese approach was that within tolerances was only minimally acceptable; it had to be as close to the actual specification as possible. This can be achieved by tracking and understanding the sources of variation in the manufacturing process.
From here we could digress into a whole long thread about reducing variability in processes, but you all can Google that and Taguchi Methods for yourselves.
The one really good example I recall off the top of my head was the transmissions that were made both in the US and in Japan by Ford and Mazda respectively (there’s some kind of partial ownership in both by each). Anyway, it was the same design, same specs, same tooling, etc., but the Japanese ones always came out running better with less test failures and so on. Investigation showed what the Japanese were taking as an assumption: that all parts had to be well within limits with minimal variation, very close to the actual specification. All the American built parts were within tolerance, but the variability was much greater. So clearly, it was neither a design fault or a production fault; it was a fault of production methods.
The Japanese track variation and make efforts to reduce it wherever possible as a matter of course. This methodology goes by a lot of names (some were very stylish in business circles in the 80’s), but it’s really quite simple and in fact is largely an American invention (reference Shewhart, Deming, etc.). The methods are used to varying degrees nowadays in US plants; my personal opinion is that Saturn in Tenessee is the most progressive in this regard (and it would appear their cars reflect it).
Of course, Japanese cars produced here in the US are normally built in accordance with the Japanese standards and methods, which would be those described above.
So note that both the domestically produced “Japanese” cars and the Saturns (and some of the other US built cars, too) come out quite well. It therefore must NOT be some kind of secret hand-twist on the assembly lines that they only know and use in the Land of the Rising Sun!
Having said that the achievement of a high standard of quality is quite possible using the methods described above, one has to consider the effect of subcontracting out the manufacture of components, especially where the emphasis is on lowest-bidder and lowest cost. They do subcontract out component manufacture in Japan, but the contract equivalents (AFAIK) always specify that evidence of statistical process controls are provided before bids are considered and throughout the delivery of the products. (I even recall seeing such evidence for cigarette lighter sockets that were sub-contracted out to some very small outfit.) A slip in quality standards is at least as bad as a slip in cost or schedule.