Indeed, AC/AE could have hardly made things more complicated.
Altitude Qualifying miles (AQM) = status miles
Aeroplan miles = award miles
The number of Altitude miles (status miles) determines your Altitude status which gets you certain benefits when flying AC (and partner airlines) - this is the status people are interested in obtaining since it comes with real benefits. Altitude is managed by AC and AC determines what benefits you get.
Since Aeroplan and AC are separate companies, Aeroplan thought it would be a clever idea to introduce status levels as well, which is "Distinction". Aeroplan Distinction status is pretty much useless except for a few minor benefits.
One may think that any Aeroplan miles earnt would qualify for "Distinction status", but that would be far too easy, wouldn't it?
Only some of the Aeroplan miles you earn (miles earnt from flights taken, flights earnt via your credit card, certain promotions) count towards Distinction status.
Or maybe to put it differently:
All transactions (buying gas at ESSO, staying at a hotel, using your AE credit card, taking a flight) earn Aeroplan miles.
Only a subset of those miles count towards Altitude status (i.e. only flights) and only some of the Aeroplan miles earnt count towards Distinction status. Altitude benefits and Distinction benefits are completely unrelated.
Or just in case you prefer a mathematical explanation:
A = Aeroplan miles
B = AQM
C = Distinction miles
D = Lifetime miles
For any miles earnt during a period T, the following is true:
B are a subset of A and C are a subset of A. All B are also C, but not all C are B. D are a subset of B and by extension A.
AND
A >= C >= B >= D
Really couldn't be any simpler, could it?
