Well, at the risk of coming across smug one is for planning and one is for actual in-flight operations.
For example, I have to plan not based on destination weather but on alternate airport weather. As soon as I am airborne, the alternate minima kind of goes out the window and we begin using charted minima.
For example, say I am going from A to B with C as the alternate.
In flight planning, I really only care about the weather at C. I mean, I care about B as well, but I know I am definitely going to end up at C if B doesn’t work out, so I plan on ending up at C, and hope I’ll make B. That way, I’m not surprised if and when I end up at my alternate.
Now in order to plan for C I have to use weather minima of, say, 600-2. That is a cloud base of 600 ft. and a visibility 2 miles. It doesn’t matter if an instrument approach at C allows me to go down to 200-1/2, I have to assume 600-2 are the minimums because that’s what the government says. It’s a little “fudge factor” that says the weather has to be better than minimums, and these alternate weather minimums differ based on the number of runways and the type of approaches at the alternate airport.
Once I’m airborne, that alternate restriction no longer applies. If airport C drops below 600-2, I’ll have to specify a new alternate airport for ATC, but I’m not restricted from trying to land at airport C with the reduced weather.
Now, why would I try for airport C and not do to the new airport D? Well, maybe C is on the way to D and C happens to be a company base where my passengers will be looked after, while D is a back-of-beyond type place that only permits me to get gas.
I should also add that, once airborne, the charted minima (less any authorization from the government) is used at whatever airport I approach, be that airport A, B, C, or D.
I hope that doesn’t muddy the waters any.