As far as I can tell, there is no noticeable difference between the tags read-mapping and alignment. Three of the fifteen questions under these two tags use both tags, and the rest seem too similar to warrant any separation.
EDIT: Clearly I had failed to notice the quite significant difference between these terms. However, the ambiguity of the
alignment tag and the way in which it is being used should be fixed. Terdon's answer below gives a good resolution of this issue.