Oh, I see what you are asking.
The testing methods are NOT comparable. Triton's testing machine (ICP-OES) breakdowns everything in the sample vial, and gives you how much calcium, magnesium, carbon, etc. atoms were in your sample. It's okay to leave Triton samples in the container for a long time. They are NOT testing nitrate, phosphate*, free calcium, free magnesium, and alkalinity.
If you are using test kits for calcium, magnesium, alkalinity, ammonia, nitrate, phosphate; these kits only measure what's in the water. So some calcium/magnesium could precipitate out onto the container; nitrate, nitrite or ammonia could get converted to other compounds, etc. Technicians/scientists store samples for later testing by putting a 'fixing agent' to stop these chemical and biological conversions. For ammonia, nitrite, and nitrate; the refrigerator should slow the conversion process.
For example, let's say you wanted to track ammonia over a week. If you took a water sample every day, but left them out, some of the water's bacteria would change the ammonia to nitrite, nitrate, etc. I couldn't tell you how slow the processes are, but they occur. Alkalinity is the one that probably stores the most poorly.
You could try an experiment by testing some water and see how the same stored-water tests out week(s) later.
Remember also that your alkalinity and pH change throughout the day, i.e. a morning alk measurement should be compared to another morning alk measurement, likewise with pH.
*From my background knowledge, the Triton Labs read-out give a phosphate measurement, but that number assumes every Phosphor atom they measure is in a phosphate ion, kinda of a worst case scenario (conservative case).