Non Linear Resonance

JenkoRun, perhaps this is may aid your understanding of the functionality of the two problems you presented:

"When do we want to build the coils to cancel magnetically and add electrically?

and

When do we want to build the coils to cancel electrically and add magnetically?"

The distinction between coils that cancel magnetically and add electrically versus those that cancel electrically and add magnetically comes down to what you are trying to achieve in non-linear or resonant circuit topologies (such as those explored in replication threads for Don Smith, Tesla, or TPU-style devices).

1. When do we want to cancel magnetically and add electrically?

(Example: Nested counter-wound series coils, bifilar non-inductive windings, or bucking coils)

The Setup: Coils are wound in opposite directions (or phased such that their magnetic fluxes oppose each other), but connected in series (or configured) so that their voltages or electric potentials accumulate rather than cancel out. 

When We Want This:

To eliminate self-inductance / reactive impedance: When you want a coil or a pair of windings to pass high current or high-frequency pulses without choking the circuit in conventional inductive reactance (e.g., non-inductive resistor/coil configurations).

To create steep gradients / dielectric stress: In many overunity/free-energy research schematics, cancelling the internal magnetic field forces the energy to manifest as an electrostatic or voltage potential rather than a trapped magnetic field.

To prevent core saturation: In transformer or dipole designs where high primary currents are pushed through without wanting to prematurely saturate a magnetic core or create an opposing Lenz's law feedback loop against the driver circuit.

2. When do we want to cancel electrically and add magnetically?

(Example: Aiding coils, Helmholtz-style configurations, or standard tightly-coupled transformer primaries/secondaries)

The Setup: Coils are wound in the same direction and connected to reinforce each other’s magnetic fields. However, depending on how the terminals are tied together (e.g., series-opposing voltage nodes or phase opposition), the terminal voltages can subtract or cancel out externally while the magnetic fluxes combine constructively in the core or space.

When We Want This:

To maximize magnetic flux density: When you need a strong, concentrated magnetic dipole to interact with an ambient magnetic field, a secondary collector, or a spatial dielectric/capacitor plate layout (as emphasized in Don Smith's core concepts where the magnetic field is the primary replicable vehicle).

To isolate electrical feedback (Lenz breaker): By forcing magnetic addition while keeping the electrical loops isolated or phased out, researchers attempt to harvest the magnetic wave propagation without drawing a direct conductive load back onto the primary source.

Summary: The Core Philosophy

The reason you see opposing configurations across different schematics is due to a shift in target medium:

Magnetic Cancellation / Electrical Addition is used when you want to bypass standard inductive choking, collapse traditional back-EMF, and convert spatial setups into high-voltage electrostatic/scalar nodes.

Electrical Cancellation / Magnetic Addition is used when you want to project a pure, unhindered magnetic dipole into space or secondary pickup elements while preventing the electrical load from reflecting back into and killing the primary driver.