I had to look closely at the manual, but I think this explains that
--strata have different meanings, but I think it would have been helpful if there were some examples where
-a wasn't added to report all alignments:
In other words, in their examples where all alignments are being reported with
-a, I think
--best is sorting the reported alignment order, and
--strata is actually filtering for the hit with the fewest mismatches. However, otherwise the manual says "When --best is not specified, Bowtie may report alignments that are sub-optimal in terms of stratum and/or quality (though an effort is made to report the best alignment)."