See our modular plugs here.

Modular plugs are designed to work with either stranded or solid conductor wire. The version designed for stranded wire has two "tines" that pierce the insulation and slip through the middle of the wire, pushing aside the individual strands. The version designed for solid conductor wire has three leaf "tines" that pierce the insulation, then snuggle alongside the solid conductor, clamping it in place.

If you use a modular plug designed for stranded wire on solid conductor wire, the tines will simply shear off the solid conductor, and will thus make intermittent, at best, contact.

When do you use solid or stranded conductor wire? The answer lies mostly in why stranded wire is made in the first place: Stranded wire is more flexible, and endures bending, flexing, and pulling better than solid conductor wire. So stranded wire is typically used in "outside the wall" applications where the cable is likely to be moved many times over the course of its life. Solid conductor wire is used inside the wall, since once the cable is laid in and terminated, it will not be moved or flexed.