On the engine vs BM debate.
Another way of classifying strategies is by their objective in terms of turn-structure: what we generally consider an engine tries to replicate a nearly identical playmat every turn (usually obtained either by drawing through most of the deck via tact/smithy/village chain/scrying pool/menagerie/library/alchemist/HP...) while what usually drives BM is a high average hand output (hence all the talks of 'moneness' in BM). Under that classification system, an action heavy deck with no drawing capacity would be 'BM'-ish. You would reason mostly in average money output of your village/merchant ships rather than in terms of deck drawing reliability. Of course the line gets blurred when you draw say, a quarter of your deck.
It's not uncommon for your 5-card hand to be a quarter of your deck well into a big money game...
I don't know that I think the 'identical playmat' thing is a very good indication of things either - chancellor/stash isn't an engine, and there are quite a few engines that have great big mega-turns... only about half the time.
I think an engine is an engine if I am chewing through lots of cards in my deck on a fairly consistent basis, roughly.
Hm, somehow, in my mind, stash/chancellor *is* an 'engine', as every chancellor play leads to a perfectly predictable next turn. It's not a BM, because the average moneyness of the deck is low. Maybe I should rename those groups and just make it a separate classification to engine/BM. My point is, they provide a pretty good metric to compare or contrast strategies differently than just 'action heavy' or 'treasure heavy'. And big mega turn decks are a (third) group of their own.
Basically, the idea is to reason in terms of the probability distribution of the money output per turn. If you try to make it very consistent and near identical from turn to turn (probably a multiple of 8 ), it's an 'engine', if you try to get the highest mean it's a 'BM' and if it is just some very fat-tailed distribution (no money most of the time, lots of money in one turn) then it's a "mega turn" deck. Then there are messier things where the distribution is all over the place.
With this classification, people have a clear objective in mind: if they go for an 'engine', consistency is in order. If they go for 'BM', moneyness is the key metric. A 'mega turn' is defined by the average time it takes to close the game.