So which is it, ferrite bead, inductor and multilayer or wound?

All different things -- ferrite bead chips are always multilayer and saturate easily; ferrite beads (various styles, wound) saturate somewhat less easily but AFAIK always at some fraction of rated current. Inductors come in multilayer or wound types, the former evidently use a low-mu or distributed gap material while the latter use a formed shape with gap built in.
- The enclosed types (multilayer, composite, molded, shielded) have good shielding, so that the susceptibility isn't much greater than an equivalent length of wire.
- "Semi shielded" types usually have some variation of a bobbin core, so the external field coupling drops off quickly with distance (relative to the height of the bobbin). It's a dipole, but it's small?
- Unshielded types are usually rod or solenoid variants and are ordinary dipoles along the axis.
- Toroids are okay, usually having one equivalent loop turn (and corresponding wide dipole) due to the winding going around the toroid itself. This is negligible if there are a lot of turns on the core, and can be canceled out if the winding doubles back on itself. Few-turns toroids have further inhomogeneity due to the relatively large spaces between turns (each loop looks like a dipole, so the whole thing looks like a (n+1)pole..).
HTH

Tim