I'm going to answer this assuming that 'stacked' was either a typo or that the article meant 'staked'.
Staking is where you put a stake (or something stick-like) in the ground by the plant, and tie the plant to it to support it.
Trellising is where you have something like a wall or panel (hog wire, a cattle panel, etc.) where the plant can climb it. Trellises are often made creatively with resourcefulness. You may have to drive stakes (or more likely fence posts) in the ground to support the trellis, too. I've heard of making circular trellises with something like hog wire that don't seem to require heavy-duty posts, though.
People don't trellis tomatoes as often as they cage or stake them, though, I'm guessing. Trellises tend to be a lot more work to create and/or set up (but they can be rewarding).
Stacking is where you put multiple things on top of each other, and as far as I know, it's not a known way to support tomatoes (although I like Colin's idea), but I could be wrong. It's not popular enough to where I've heard about it, anyway.