The biggest difference between straight and rolling count is when the weight transfer between the beats happens: either directly in the middle of the beat, or closer to the upbeat. However, there is another significant difference between the two forms of counting. Each method of counting naturally links the & with a different beat of the music.
In straight count, the &s belong to the beat of music immediately beforehand. For instance, in a straight triple, the & count is connected to the downbeat. Instructors often refer to parts of the triple this way; a tuck turn compresses during the & of 3 before sending the follower out on 4. The only thing happening on beat 4 is the step out; it is beat 3 that is shortened because of the presence of the triple’s &.
We can see the connection even more clearly in the straight count quad rhythm. In the quad rhythm, there are 2 beats and two elements between beats. Both of the & counts occur after their respective beat, so the beat of music ranges from, e.g., 1 to the & of 2.
In rolling count, the relation between the & (as well as the a) and the beat is reversed. In rolling count, both the & and the a belong to the beat that comes next. In a rolling triple, the a draws into the upbeat. In our tuck turn example, the dancers use the compression of the a to send the follower into the 4.
The difference is extraordinarily clear with the rolling quad rhythm. Instead of having the & counts come after the beats, the a counts appear before each beat. Thus, the rolling quad goes from, e.g., the a before 1 to 2.
If you have ever wondered why some teachers count rolling count starting with “&a1&a2…” rather than “1&a2&a…”, now you know why. In rolling count, the &a belongs with the following beat, so starting the count on the beat is akin to leaving off the first syllable of a word.
But why does this difference matter? Well, it turns out that west coast swing just works better if the &/a count belongs to the following beat, like it does under the rolling count. First, starting the beat on the & allows the center to initiate its movement before the body has to land on the new foot. If instead the beat starts on, e.g., 1, and you are supposed to land on your new foot on 1…there’s no time to move the center, and as a result the movement looks clunky, mechanical, and march-y.
Second, at a higher level the & provides time to build momentum for the next movement. The most common example of this is stretch; the stretch before the 1 of each pattern occurs at the start of that pattern, during the & and a. The stretch is not attached to the anchor; if it were, the last pattern of the dance would have energy built up with nowhere to release it, and there would be no initiation on energy for the first pattern of the dance. Pros extend this concept to almost every aspect of the dance: they use the & to build energy for accelerations (which clearly belong with the accelerated move), they stretch in order to resume the dance after finishing playing, and they use the & in order to build energy for turns, as in a tuck (&4) or a pot stir (sinking into the & to release on 5).
Finally, linking the & with the following beat helps create the pulse of the dance. West coast swing is built to finish a movement on the upbeat. (If you don’t think so, try doing a kick-ball change. Now try doing a ball change-kick. The timing is the same, but one of those will feel good and one will feel awful. It’s not just you.) By attaching the & to the following beat, the 2-beat increment finishes on the upbeat and thus naturally fits the pulse of the dance.