"Through", like "fast", is not tightly defined, so people can have different ideas of what it means.
Personally, I associate "tippier" rods with smaller, fast-biting fish, and more "through" with fishing for bigger species when playing them is more the issue. Of course there are some excellent rods that contrive to combine fast striking and forgiving tips with non-locking playing actions.
The only rods I've had that were really "through" weren't so good in practice. I had a Berkely Tri-tip Barbel rod (tackleshop bargain) that looked nice but was hopeless at playing barbel. You'd find yourself with the handle pointing behind you and the fish still doing what it liked. Another through action disappointment was a Shimano float rod I bought from someone who imported it. Made for the US market, it was a beautiful, slim, cork-handled classic design with a line rating of 6-12lb and I fancied it as a barbel float rod. But when I tried it out in the close season on ordinary commercial carp of 5-8lb, it just wasn't powerful enough in the butt, and you had to splint the rod well up the blank with your reel hand to pull a fish up. The high line rating proved very questionable.
More positively, I've had great value from a couple of Carbonactive Asaki float rods that have proved tippy enough for roach and elastic enough for small to medium size tench.