Beading wire is a stringing material made up of numerous, thin steel wires that are woven or wound together. It's often coated with a thin layer of nylon that helps protect the beading wire from wear and deterioration and gives it a softer, more supple feel. Nylon coatings can be clear or tinted.
As a rule, beading wire containing a larger number of woven strands is more flexible than beading wire with fewer strands. Better flexibility means less kinking and better jewelry drape.
A traditional example of beading wire with a small number of strands is tiger tail. Tiger tail is economical and typically very strong, but it can kink easily when you bend it. Depending on the brand, tiger tail may or may not be coated with nylon.
Over time, you'll develop a feel for how to select the best size and strength of beading wire for a given project.