1050 is a simple steel with about 0.5% carbon (mid-range, very sufficient for swords).
Terms like spring tempered and spring steel get thrown a lot so the semantics of it tend to get blurred and difficult to discern accurately, but here's a basic synopsis
Spring steel is steel that is from a spring or is used for a spring. Typically this refers to automobile springs and the like, and you will see many references to 5160 as a common "spring steel."
As is, spring steel is just steel. There are no special qualities that make it any different from any other steel. When steel is in an annealed, or soft state, it is relatively easy to carve, grind, bend, et cetera. Then, it is heated and quenched, and the resulting transitions in the steel "harden" it. This may be a bad analogy, but think in terms of plastic and glass. The plastic can take but will not maintain an edge because it deforms easily and is not resistant to abrasion. On the other hand, glass can maintain a wicked sharp edge, but is not as flexible. The same applies to soft and hard steel.
Blade steel hardness is typically compared on the Rockwell C scale. For instance, an annealed soft blade steel is often around 20-30 RC. Hardened blades typically run from 58 to 62--sometimes more, sometimes less.
But to retrace our steps... We have our steel hardened and it will hold a great edge because it's hard, but the result also leaves us with a blade that will not flex a great amount laterally before snapping, and if you whack the edge against something, it could chip like a razor blade. This isn't necessarily a big problem but it tends to play a common role in swordmaking. In the spirit of avoiding technicality, the reason steel gets hard is because its molecules are very stressed. To alleviate that stress, there is a process called tempering. It involves heating the blade to a certain level for a certain time. One effect is that it gradually reduces the hardness of the steel a small amount, but many feel that some tempering is well worth that cost.
"spring tempered" is a term in the sword world that's often used to describe steels that are tempered back to the low or mid-50 range RC, softer than your typical good quality knife blade. The side effect is that they are not extremely stiff or capable of holding a spectacular edge, but are very capable of being flexed without retaining a bend. This results in a very "tough" blade.
Sorry my explanation wasn't very technical or specific, but I hope that clarified the issue a little.
As far as the CS Chinese War sword, I haven't handled one so I don't know, but considering the maker that provides those swords (Fred Chen I believe still does them), I would assume it's pretty good quality. However, you could always look at Hanwei's offerings, they may have something you like for a decent price. I'm thinking someone will probably recommend Kris Cutlery, but that depends on if they offer anything you like. Himalayan Imports, again I don't think offer a "Chinese War Sword" but their work is well-regarded for its toughness, so if you are not very specific about the type of sword you're looking for, feel free to shop any of those choices.