The difference between kishoutenketsu and Western twists... I hadn't thought about that before. I can think of a few differences, though.
Have you ever seen a yonkoma manga? They're four panel comics that normally follow kishoutenketsu structure. The idea is that the first panel is ki, the second is shou, the third is ten, and the fourth is ketsu. So the panels usually work like this:
Ki: A scene is set.
Shou: Elaboration on the scene from the first panel.
Ten: Climax, an unforseen event that doesn't have to do with ki and shou directly
Ketsu: Resolution, effects of third panel on first two panels.
If you flesh out Kishoutenketsu to a TV show or something like that... the difference between a Western twist and the Kishoutenketsu is that Kishotenketsu doesn't have conflicts written into them. But Western twists have conflict written into them. Let's use your example to determine the structure of a Western twist:
I’m thinking, for example, of the way many American police dramas (such as Law & Order) adhere to the following structure:
The viewers are introduced to the crime, the detectives, and the initial suspects.
One of the suspects is captured and it seems like all the evidence points to him/her.
Surprise! New evidence comes to light, or someone makes a confession, that destroys the prosecution’s case.
A fresh round of investigation reveals the true criminal, who is brought to justice.
This structure works like so:
Act 1: Introduce a conflict
Act 2: Builds on act 1
Act 3: Twist based on acts 1 and 2
Act 4: Resolution based on twist from Act 3.
So it sounds like Kishoutenketsu, but the major difference is in the twist, which you've noted. However, act 4 and Ketsu are also changed because of the twist/ten. For Kishoutenketsu, ketsu is the sum of all the parts-- what happened in ki and shou plus the seemingly unrelated third act come together in the end. But for Western twists, Act 4 is based almost completely on act 3, though it's resolving a problem from either act 1 or 2 (depending on where the problem originates, in Law and Order conflict is usually set up in act 1, but some cartoons/pilot episodes set up the problem in act 2 and use act 1 to set up the setting and characters). It doesn't really sum everything up... per se. Examples would help, probably so here you go!
Kishoutenketsu (for the most part) has two acts that are "straight", by which I mean they follow each other logically. For example: if:
ki is "a boy sees a vending machine",
shou could be "boy buys soda from vending machine, receives drink".
But ten doesn't have to be related to ki or shou at all. It can be disconnected (it usually is disconnected). So:
ten could be "boy goes into his house".
Ketsu would then be "boy notices the same soda he bought sitting on the table in his house".
Ketsu brings the three acts together by showing the effects of the third panel on the first two. You can't really compare ki and ketsu, the connection between the two isn't apparent unless you know what happened in shou and ten.
In the western style:
act 1 is "boy sees vending machine".
Act 2 is "Boy buys drink from vending machine," but there's no conflict if he just gets a drink. Act 3 is a twist based on act 1 and 2, and act 1 hasn't brought anything up but the vending machine. Act 2 needs to build on act 1. In Western style writing usually has the protagonist in conflict with something-- in this case, the vending machine. So:
act 2 would probably be "Boy buys drink from vending machine, doesn't get drink"
as that is a legitimate way to build on act 1's situation. But Act 3 probably isn't "boy goes home," since that isn't based on act 1 and 2. What's more likely to happen is:
act 3 is "boy kicks machine"
or something like that. Then:
act 4 as the resolution would be something like "boy gets drink".
Act 4 resolves the conflict in act 2, but it doesn't really unify acts 1 and 3 much. I mean, act 1 is just the set-up for act 2, and act 3 is the "defeat" of the problem laid out in act 2, but act 4 doesn't really unify everything. Act 1 and Act 4 could be compared to show what the story itself is about. The protagonist was without a drink (act 1) and becomes a protagonist with a drink (act 4).
That doesn't really explain the "without conflict" part of it because I picked a pretty bad example, but... in the kishoutenketsu example, there's no real conflict. Think about it-- there's no struggle, there's no fighting, there's nothing fundamentally "bad" happening. It's just a situation at hand. I mean... the protagonist isn't really "against" anything, right? He's just buying a drink and going home. But in the Western example, the protagonist is against the vending machine. The machine denies him a drink and he "defeats" the machine. There's conflict there.
There are probably other differences between the two, but I'm not well-versed in kishoutenketsu as far as TV shows/movies are concerned... I've never noticed this structure in a show, is what I mean. But I don't watch much Japanese TV since I'm not in Japan (I've watched Japanese movies, but I don't know if it's applied to movies). I do notice it in books (and manga) though, and for the most part it follows a similar structure to what I've explained here.