Mr. M's train is stationary. Molly & Mrs. M approach.

Now, this moves pretty fast even though we have, in our thinking, slowed the velocity of light down to something like a hundred kilometers per hour. (Or, you may use a hundred miles per hour if you prefer to think in terms of the old English system.) At any rate, the train speeds we are thinking of a bit faster than half the velocity of light. I have a glimpse of Molly's school when the lightning struck before the animation starts over just to illustrate where in the animation the following still takes place.

For Mr. Modern, the distance from Maple to Dixon is less than the  proper length of his train, while his wife's train is even shorter. As we shall see, the relativistic length of anything that is moving decreases as the velocity approaches the velocity of light.

From Mr. Modern's perspective, the light reflected from the caboose and locomotive of his own train reaches his eye simultaneously -- assuming he is standing in the exact center of the train. His wife's train is something else again. First light reaches her caboose, while it is still traveling to catch up with her engine.

Then light reaches her locomotive.

Thus simultaneity is a matter of perspective.

Now this lack of simultaneity between the caboose and engine of the other train,  will be observed by all the folks on Mr. M's train. Everyone in his frame of reference, in the world of his moving train, can agree on what is meant by "at the same time." The engineer in the locomotive, the break man in the caboose, and the conductor collecting tickets somewhere in between can all agree on the proper time in their frame of reference. Their clocks can be synchronized.

They may see the light at different times but that is not the celebrated time desynchronization of Einstein's relativity. What they see is desynchronization due to signal transmission delay time. That kind of desynchronization was understood long before Einstein, and they can account for it. That is the difference between observing and measuring.

So while only sees his engine and caboose leave burn marks simultaneously if he happens to be the same distance from each of them, he can would measure the same result even if the distances were different. We will see that the engineer in the locomotive and the brakeman in the caboose can measure their burn marks as being at the simultaneous in proper time even if their observed time is different. To measure, he could compare observations using identical clocks at different locations. These identical clocks must, however, be at rest relative to each other. 

Moving clocks, however, are a different story.