It's not necessarily higher grade, but usually a thicker gauge.
A 1/4" cable carries two conductors. In the case of a line level cable and assuming also unbalanced(one ring), then it's Tip for Hot/Signal and the sleeve part is a shield for helping keep out outside interference like RF. The signal is most likely a 24-22 gauge cable with a PVC insulator, while the shield is a braided or semi-braided(or sometimes foil) that goes around the ouside of the insultated signal cable.
In the case of a 1/4" speaker cable, it's not the same. There are two insultated conductors that are of equal gauge. There is no shielding. Red goes to tip, black goes to sleeve. Substitute white for red, I've seen it a lot. As has been said, this cable is thicker and heavier since it is carrying an heavier current of an amplified signal.
In a pinch, you could use a line level cable for speakers, but it is going to not give the performance needed and could cause problems all around, from the amp to the speaker, to the wires/conductors overheating and melting down(yes, I have seen it happen). It's also going to give you a loss of control on the driver, giving you wonky performance, less bass and more prone to kill drivers, especiall your highs. Amps aren't going to like this wildly varying resistance load either. Likewise, you can use a speaker cable for a line-level device, but expect extra noise in longer runs and wacky thing to happen when using it on devices with active pickups.
I have some speaker cables that look identical in every which way to a line level cable since those are meant for less than 100-watts. I have these cables not only clearly labeled but REMOVED from my inventory so as to not cause confusion in an event. The speaker cables I am using are Speak-On to 1/4" and are rather heavy so there is no chance for confusion.
Personally speaking, I do not like 1/4" for speakers, especially 1/4" to 1/4" since it can look just like a 1/4" instrument/line cable. However, many of the better speaker cables will be using an over-sized covering on the 1/4" cable, you know, that part you can screw off to access the connections for repair?
Whatever you do, LABEL the cables so as to avoid confusion. As a minimum, label the speaker cables and label BOTH ENDS too, just to be safe if you don't neatly wrap your cables between events.
Bottom line: Will it work? Yes, it can work. The actuality is that just don't mix and match. Use the right cable for the right job. It's one thing to use an unbalanced cable instead of a balanced and vice-versa, but we're talking line/signal levels here, not high wattage amplified outputs.