Do airlines assign a specific fare cost to each fare class. For example, if I wanted to fly SFO-ORD on United, would (made up scenarios) A or B or something else be correct.

A)
N fare is $90
G fare is $100
....
Y fare is $2,000
Lowest fare available can be controlled by availability of fare classes

B)
N fare is cheapest
G fare is 2nd cheapest
....
Y fare is most expensive
Lowest fare available is set and UA somehow decides which fare class that it will release into.

I was pricing out an SJC-PHL on UA and it was about $250 one-way, and I was shocked when I got to the payment screen and the flights were both in N because I had bought tickets on this route for half that price in N.

B is more correct (in that there is no set price for a particular fare class on a particular route, but there tends to be an order of cost for different fare classes), but it's really a mix of the two (in that the fares themselves can change, especially from one day's flight to another day's flight, but on a particular flight on a particular day the changes come more with control of which fare codes are made avaible when and which fare codes aren't).

Not all fare classes are always active. Some have restrictions such as N-day advance purchase (and diappear automatically when it's less than N days from the flgiht), others the airline may simply choose to disable or enable whenver it wants to for a certain flight.

Also, they're often called "buckets", because the ailrine will often only allot a certain number of seats to each fare code or "bucket", and once that "bucket" empties out, the next-most-expenive "bucket" appears as the cheapest-at-that-point.

Also, there are sub-fare-codes, which only certain websites* let you see. So there might be an N45W21 code and an N46X07 code that are both technically N, but might have different restrictions and pricing. In this example, who knows what the 45/46 and W/X mean, but the 21/07 is the number of days in advance of the flight that the code expires.

* I use expertflyer.com, which is a paid site. There may, however, be free sites that let you see all the fares available for a given flight, but since I use this paid site (which I pay for for other features it has), I don't know what the free sites, if any, would be.