Climax arranges terms in ascending order of importance, intensity or scale, so that each item exceeds the one before it. The sequence builds, and the final element carries the weight the arrangement has been accumulating.
In its strict classical form each clause also picks up the last word of the preceding one, chaining the series together.
Paul, in the King James translation: “tribulation worketh patience; and patience, experience; and experience, hope.” Each term becomes the subject of the next, and the sequence climbs from suffering to hope without a step that can be skipped.
The chained form, where each clause begins with the previous clause's final word, is gradatio. Climax without the chain is simply ascending arrangement.
Climax persuades by implying that a progression is natural — that each step follows from the last and the destination was always where the sequence was heading. When the steps genuinely follow, this is clarity. When they do not, it is a slippery slope with better manners.
The resemblance is close enough to be worth stating plainly. Both figures present a chain of steps ending somewhere distant from where they began. The difference is that a climax is describing an order of magnitude, while a slippery slope is asserting a causal sequence. A reader should notice which is being offered, because the arrangement looks the same either way.
Climax also has a practical constraint that other figures lack: it can only be used once per passage. Having ascended, a writer cannot ascend again without starting lower, and a second climax in the same section reads as anticlimax — the sequence arriving somewhere the reader has already been.
