I can't say about your Giant and Trek. The "Bell Brand" cable kits one can buy at department stores are not lined, and I believe use galvanized cables. I assume they are similar to what some department store bikes use.

If you are replacing the cables, you can look at the ends of the housings if the ferrules aren't crimped on, and see if you can see the liner. Or, perhaps feel how the cable goes into the housing. Smooth, or hitting the ribs?

Also look at the cable housing to see brand and model markings.

Coated wires should be easy to identify.