I'm using the parlance of UCB's upcoming book, and its how they use their terms. Assssscat's are premise based, which means the audience knows what it is based on, that they are latching onto ideas everyone has seen and heightening. Organic scenes are from scratch, just a suggestion if that, and necessitates the troupe working in its first year at least three times a week for rehearsal (something I feel would be an aberration here, rehearsing that often), but yes, I see how 'premise' as we'd define it is exactly as you say.
They also have a radical redefinition of game, and I think if you are open to listening to improv podcasts you'd see quickly what I am taking long in confusing the issue... if you don't mind: http://ucblongform.libsyn.com/rss
>> The Achilles Episode
(I took an intensive with him and it was mind blowing) is a good example, if only because they, if I recall, use several of their reworked definitions and, I think most demonstrative of how they believe things should go, as they try to show the "right way" to do the pattern game, something UCB takes more seriously than absolutely anyone here possibly can (going A to C is the point, and though I agree, I can't really apply that standard onto others like they can... anyway, for them, if you aren't low level and you do A to B (and even if you are low level, honestly, WTF?! Have fun retaking 201!). In other words, if I go 'Salt' pointing to you and you say 'Pepper' their philosophy is that you are offering absolutely nothing, three thumbs down, you epic fucking failed... needless to say, it would be wayyyyy past the point where I should condescend to yesand anything but calling your offering out... as an onstage coorelary, there's the oft-cited: "I am SO mad at you.... UNFORGIVEABLE" and partner responds, "Here, have an apple" so the goodnatured improviser thinks, "I must yes and" and so goes on to say, "Ok, thank you, I'm calm now." No, according to UCB, you just said "no but" to yourself, the correct response would be, "I see your fucking apple, how's that to make up for you getting us thrown out?" or whatever.
Sorry again for the length, but you pointed out something that in Austin would be accurate but would be, if not baffling, not right to those writing their curriculae, and since it IS the only curricullum that is accredited, perhaps there is something to it. Organic scenes can involve game, and so do relationship scenes, even scenes with a narrative arc. "If this is true, then what if" is their sketch-to-improv concepts to be used in conjunction with improv...
Keep in mind also that monoscenes, the form where everything either takes place in one place,* are organic shows (except when Roo Roo does their "worst thing ever" audience interviews, in which case, its premise based)... http://www.ucbcomedy.com/podcasts/ucbtny
>> I think you can still go here and listen to my favorite Roo Roo, Gemberling, though the Besser interview goes into unboring things. I'll not mention which shows talk, way back in 2010, the financial and tax advantages to setting up theaters certain ways, but you should find most of these enlightening, though I know most people have heard all this stuff before.
*Not really, but when all improvisers are onstage, they are in same reality and same room, though there are split scenes and time dashes I've seen sometimes, including the infamous 9/11 show alluded to in Gemberling.