Inspired by this question: what does the "sequence number" on an airplane boarding pass signify?
It's the order in which you checked in to the flight segment. The first person to check in will get seq 001, onwards up to the last person who checks in.
That does not make it the same as the order in which you obtained your boarding pass, although in most circumstances you would receive a boarding pass at the same time as you check in.
If you obtain another boarding pass it will have the same sequence number (unless for some reason you were offloaded from the flight in the mean time), even if printed by another airline.
Some people competitively attempt to obtain sequence number 001. I suppose everyone needs to have a hobby. [In some cases it is relevant, for instance for a while British Airways prioritized upgrades by whoever checked in first (amongst other considerations), and United Airlines uses it as a tie-breaker if two people have otherwise equivalent precedence for an automatic upgrade.]
The Apollo computer reservation system does not use sequence numbers.