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There are generally 2 types of miles. Unfortunately they have different names in the various programs.

1) miles for purpose of elite status
2) miles for purpose of awards (the so called free tickets and upgrades)

Typically some promo bonuses, flying on non-alliance airlines and miles earned from non-flying activity (eg credit card spend) fall into the second category. However some programs will count some or all of these examples in the first category.

In most programs, all miles earned in the first category automatically count for awards as well. But some programs have points or credits instead of miles to determine status.

So in the example you posted, the 4000 bonus miles fall into the second category. I am not familiar with all the rules of AAdvantage but credit card spend does count for the various lifetime statuses.