There is a discussion of stranded vs. solid wire for speaker cable here. The consensus (or at least the weight of opinions) seems to be that there is a theoretical difference, but no practical difference.
Speaker wire is also called lamp cord. It is basically parallel stranded wire in either 16 or 18 gauge. The lower number indicates the thicker wire. 16 gauge is thicker than 18. The difference in gauge has to do with how much voltage drop (and in music, signal loss) there is over long distances.
Numerous comparisons seem to indicate that basic speaker wires (and wire sold as lamp cord at even a lower price) are indistinguishable from exotic wires.
If it is a long run, 16 gauge is preferred. If the run is very short, you probably can use 18 gauge with no apparent difference in sound. But the cost difference is fairly small, so 16 gauge is preferred.
There is no shielding on speaker wire, so the covering is of little import. Solid wire is much harder to handle (less flexibility), so stranded is preferred for audio applications.
While the barostat wire is solid and the speaker wire is stranded, it is highly unlikely you can get a measurable difference in signal between the two types. If it's already installed, and the run is not too long (20 feet or less) you probably can live with it. If the run is much longer, you might want to swap both wires out for a heavier gauge (16).