Steam Engine Cylinder Timing

I’m wondering about steam engine trains. There are two cylinders driving the wheels - what is the timing of these? Are they synched together, 180 degrees out, or some other timing? If they are synched, how are they coupled? Is the axle between the drive wheels solid or is there some sort of other coupling?

I’m not sure what you mean by “two cylinders driving the wheels” but that could be because I’m not that familiar with steam locomotives.
Here’s how a steam engine works though.

Go down to the second picture and hit play.

An ordinary 2-cylinder steam locomotive kept the drive wheels on either side “quartered”…90 degrees apart, and yes, the axles were solid. In normal practice, engines “led” with the right side, that is, the right-hand cylinder power stroke was one-quarter turn ahead of the left. If the right-hand drive rods were at their lowest point, the left-hand rods would be at front dead center.

while a 180-degree difference would seem to be more balanced, this was not used for the simple reason that it would allow the locomotive to be stopped with both cylinders at dead-center, making it impossible to start again without a push from an outside source.

There were also some three-cylinder engines, where the third cylinder drove to a crank at the center of the axle. These were generally synched at 60 degrees.

This Wiki article has a useful animation (scroll down to Steam Circuit). It shows an engine with a double-acting cylinder that gives two power strokes per revolution of the drive wheels.

The article notes that (as you’d expect, and as SS says) with this setup the two sides of the locomotive are 90 degrees out of phase, yielding a total of 4 power strokes per rev.

The cylinders are double acting, so 90 degree phasing provides one power stroke every 90 degrees…like a V-8 automotive engine.