Great question! My explanation of the 2...
Mainline or manifold (same in my mind) is the manifold of the 2 main branches after the top apical meristem is cut away (topping). So instead of having the one main cola you will have 2. Now you can tie down all the side branches from those 2 “main lines” to creat multiple even colas, like I did to create a bowl shape.
Quad-line info has been passed down to me by my main mentor
@Asesino85 who deserves OG credit. This technique allows a screen less scrog look. The difference is that the focus of energy is on 4 main branches after topping rather than 2 or 1. A proper quad has the 5th node topped and the bottom 2 nodes cleared away (cut). All that’s remaining is node 3 and 4 creating a criss cross or quad line. These are the 4 main branches that will allow growth for multiple even colas at the end. Check out Ase’s journal for proper technique LOL or I can help when your ready to start
After doing both, I will always choose a quad! You get a similar look with less work overall. All my plants are quad trained unless otherwise specified (I love to experiment)