Good work @lordneroo, that's a great explanation.

This is probably oversimplified, but this is how I understand the projections:

• Mercator - the poles are stretched out
• Transverse Mercator - avoid stretching, instead allow the map to tear in 3 places
• Lambert Conical - avoid stretching, instead allow the map to tear in 1 place.
• Stereographic Azimuthal - allow the equatorial regions to stretch