What a great question. I hope I can help. I think the biggest difference between sinuous springs (zig-zag) and coil springs, is the stress they put on your furniture frame. Zig-Zag springs are applied to your furniture from front to back. They have to be stretched into place and measured so they leave a crown. After application they are constantly pulling on the front and back of your frame. I have seen these bow a wood frame on couches and chairs. You can choose zig-zag springs in various guages (thicker being stronger and more stiff, thinner being bouncier and more flexible). If you have a soft wood, you’ll want to use a thinner guage, but if you use too thin of a guage, it may not support the weigh of humans the way you want it to. They can cave in instead.
Coil Springs put the stress evenly across the top of the frame. Meaning it’s pulling all 4 sides equally (from 8 directions!), and the weight is evenly distributed. You are much less likely to see this effect the frame in the same way.
Each can produce different seat shapes too. Springs can create a flat surface or a crowned top, likewise zig-zag springs make a dome top, but you have to rely on edge roll to bring the frame flat with the surface if you’re using a removable cushion.
Thant’s just based on my lived experiences. I am self taught and I also have difficulty finding comprehensive educational resources about formal upholstery teachings.
I hope that was helpful!
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https://lullco.co/collections/in-person-upholstery-workshops