The difference is that one has a self-explanatory name (linothorax meaning "linen cuirass") while the other one is obscure. The spolas is very rarely mentioned, and it's not clear from the context whether it is in fact a piece of armour or simply a garment of some sort. The idea that it is armour depends entirely on a gloss by a very late lexicographer, which claims that the spolas was a leather jerkin. If this is right, the spolas was indeed a piece of body armour made of leather; if, however, this late author was only interpreting earlier texts from context, just like we are, we might suppose it was not armour at all, but a thick linen outer garment instead. Either way, we have no idea what it looked like, whereas the linothorax is very widely depicted.

There is endless discussion among reenactors and enthusiasts about whether both spolas and linothorax were made of linen or leather, and how they were made. Because the ancients don't describe outright how to make or use either piece of equipment, a lot of what we think they were is down to what we find probable or what we can plausibly reconstruct. This is why Wikipedia's descriptions will be a bit confusing.