I guess I didn't post the question very clearly, but you all have given the answers I sought. When buying economy on a TATL an upgrade gets you up one class into business class. If you redeem 50K miles, you sit in business class.
When buying on AA Economy (or MCE), an upgrade gets you into Business Class.
From what I can gather, with BA the process is different and was less clear to me because they don't call their product "business class." The flight I was interested in, BA 226. It lists four classes of service; world traveler, world traveler plus, club world, and first. My understanding is that if you buy economy on BA an upgrade moves you up one class from world traveler to world traveler plus, not into club world.
That is correct - WT+ is sometimes referred to as "premium economy". It is a separate cabin area with different seats from WT or CW.
On AA, one step up from economy is business class, or one notch below first class. On BA one step up from economy is not club world, it is just world traveler plus. I wasn't sure if BA considers a 50k AA mile redemption something that moves you up one notch from world traveler to world traveler plus, or up two classes of service to club world.
BA and other airlines consider a Business Class redemption to be for Business Class - on BA, Club World on longhauls, Club Europe on shorthauls. You are not moving up from anywhere.
From what I gather from the responses I received, a business class ticket on BA gets you into club world seating. I would not make a 50K redemption if it only puts someone one class forward from world traveler to world traveler plus, but I would for Club World. The fees of course are a consideration, but are worth spending sometimes, rather than having to redeem 100k miles to fly AA when they don't have saver awards.
A 50,000 mile redemption puts you into Club World on longhauls, on Club Europe in shorthauls; you will pay very hefty fees in addition for using BA for your redemption.
It would have been simpler if Club World was also called business class, but I didn't want to make any assumptions on what business class means to BA since that's not what they name their product. Everyone's help is appreciated.
Airlines may vary the names they use for different classes - Iberia is Business Plus, Air Tahiti Nui it's Poerava Business, British calls it Club World or Club Europe, as mentioned previously. But Business is Business, Premium Economy is Premium Economy - though AA varies "Business" and "First" names domestically and on domestic three class flights.