Here's what I think Mike. The difference is the timing of the run for biologists and fish counters, the time spent in the Columbia before spawning for the fish, and the amount of oils in the flesh needed to arrive early for spawning for the benefit of the fish keeping fisherman. There may be some difference in the area of the river the fish are headed to.
I believe it is run timing based on statistical bell curves. From some of the reports I've read, the counts for each run taken individually fit a bell curve. When you add the curves together you get a great match for the yearly counts. These bell curves can be summed up (cumulative count) and they have a distinctive shape. This allows the fish predictors to know when the run is about half over and how much the final count is likely to be.
In general, the farther an adult fish goes up river to spawn, the earlier it enters freshwater from the ocean, hence the name spring, summer, and fall seasons as to when they enter freshwater.
Spring Chinook display more of a stream type juvenile life stage and are subject to more freshwater rearing habitat during this stage (multiple years) while fall Chinook are more ocean type, meaning they migrate seaward sooner (often during their first year) and have more juvenile growth in estuary/brackish/salt water.
As for the actual fish counts at Bonneville Dam, Spring Chinook are counted from March 15 thru May 31. Summer chinook are counted from June 1 thru July 31. Fall chinook are from Aug 1 to Nov 11. Upriver dams start counting a week or so later for each species. Following is a link for this info.
BDD pretty much nailed it. In addition those earlier fish entering tend to spend more time in the year before spawning. Obviously it requires more energy to migrate further and stay alive longer (remember they do not feed while in the river) which means when those fish leave the salt those spring Chinook have much higher fat/oil content then those later entering stocks. Those higher fat levels equate to a fish with higher table quality.
The is the reason that prior to 1900 the commercial fishery on the lower Columbia targeted those Spring Chinook and initially did not bother with those later stocks. It was only after the spring fish were depleted that the fishing focus on later Chinook stocks and sockeye and eventually coho and steelhead. Even today those springs bring an incredible price on the market. This spring the fillets from the first commercial opening in the Portland fresh markets were selling for $46.99/#. It is also why those fresh spring Chinook are consider the best table fare available by many PNW anglers.
One of final biological aspect of the various races of Chinooks is that the earliest runs tend to spawn earlier than the other stocks. That is thought to be due to the cooler water temperatures found in the upper portions of the watersheds used by those springers. With the cool water it just longer for the eggs to develop to hatching and eventually fry emerge. The end result is that the young fry from the various Chinook stocks all essentially emerge at the same time each spring.