Such an in-depth, far-reaching question as this really does deserve a response, so here are my thoughts on this matter for what they're worth;
Steps are generally only a few in number - steps to a front door for example - as compared to stairs which are indoor and tend to be higher ie connecting different floors.
Stairs is an abridged form of staircase (or stairway) and the term 'case' implies an enclosed/encased structure which is the norm with indoors.
Stairs tend to be of a solid structure - having tread, sides and riser - as compared to steps which tend to have just an open tread.
Let the debate begin. . . .
Another thought - Why do we park on a driveway and not drive on a parkway?
Why is there only one monopolies commission.....the list of stupid questions is endless
Bored now