[Steven Smith]

I looked for a good video or diagram to show you, but I can't find what I'm looking for. I'll give it a shot via words, but a picture might be needed.

What's the difference between roller and rollerless chain?

Per the Wikipedia link you posted, on the schematic under variants in design, it is the presence or lack of part #5, the roller. In #25 or #35 chain which covers most FRC applications, there is just a bushing. If you look at the #25 or #35 chain, you can actually see a slit in the bushing, and if you grab the bushing with needlenose plies and try to rotate it, you will see that it doesn't easily move in reference to the inner plate. The primary movement you see/feel is the inner plate moving relative to the outer plate.

If you did have a roller, it now be a "bearing", in that the roller could also rotate and spin freely around the bushing.

Why would one want 'rolling' bushings instead of non-'rolling' bushings?

Mostly for sprocket wear. This is where I could use a better picture, but look at this basic one here, and picture that sprocket is being driven by an outside force causing it to rotate clockwise. On the top, the chain is contacting near the midpoint of the sprocket tooth on the bushing as the tooth engages the chain. The chain then gets pulled into the root between the teeth, and then comes back out on the slack side. With a bushing, this is all sliding movement between the bushing and the sprocket, causing more wear than if you had a roller.

I notice that most sprockets on Andymark use x5 chains. Is there a reason for this?

In the "lighter" series chain, the benefits of the rollers are less important. Even at "drivetrain speeds" our chains are usually run in the low to mid hundreds of feet per minute, which is reasonably low versus their rating. Additionally, you might only run a robot for 5-50 hrs in its lifetime, versus a car, or motorcycle, or fan, etc. that might have 1000-10000 of hours in its lifetime. The sprocket wear is likely dominated by material choice of the sprocket, tension of the chain, etc, not by the presence or lack of a roller.

Good question though, forced me to revisit the topic myself and play with a bit of chain Others, feel free to correct me if I missed something.